ADAPTIVE SPATIALLY-DISTRIBUTED WATER-QUALITY MODELING: AN
APPLICATION TO MECHANISTICALLY SIMULATE PHOSPHORUS CONDITIONS IN
THE VARIABLE-DENSITY SURFACE-WATERS OF COASTAL EVERGLADES
WETLANDS
By
STUART JOHN MULLER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2010
1
© 2010 Stuart John Muller
2
Dedicated to everyone, for everything, truly. But most of all, it must be said, for Julie.
Elen sila lumenn’ omentielvo.
3
ACKNOWLEDGMENTS
I thank the USGS, SFWMD, and UF for fiscal support throughout this journey. I
thank my committee: Dr. Greg Kiker, for being the original spark that has lead to so
much light; Dr. Andrew James, for his vision for TaRSE; Dr. Mark Brown, for his
example and his conversation; Dr. Jim Jawitz, for his support, both personal and
professional; and dear Dr. Rafael Muñoz-Carpena, for the commitment of his generosity
and the conviction of his faith, which have given me more than any Ph.D. is really
supposed to. I thank my incredible family for persistent genes, boundless opportunity,
an enquiring mind, and an open heart; my cats for the peace of their innocence when I
had to let mine go; my friends for making life what it is, even when it isn’t; and my Love
for being so patient, and so kind, and so adorable.
4
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...................................................................................................... 4
LIST OF TABLES ................................................................................................................ 9
LIST OF FIGURES ............................................................................................................ 10
LIST OF ABBREVIATIONS .............................................................................................. 14
ABSTRACT........................................................................................................................ 15
CHAPTER
1
INTRODUCTION ........................................................................................................ 17
The Southern Inland and Coastal Systems of the Everglades: A Region at Risk .... 17
Opportunities for Spatially-Distributed Mechanistic Modeling of Phosphorus in
SICS ......................................................................................................................... 20
Hydrologic Modeling of SICS ............................................................................... 20
Water-Quality Modeling of SICS.......................................................................... 21
Model Selection .................................................................................................... 23
Important SICS Modeling Considerations ........................................................... 25
Model Relevance ................................................................................................. 27
Research Questions and Objectives.......................................................................... 28
Research Questions ............................................................................................ 28
Objectives ............................................................................................................. 29
2
FUSION OF FIXED-FORM AND FREE-FORM MODELS FOR ADAPTIVE
SIMULATION OF SPATIALLY-DISTRIBUTED WETLAND WATER-QUALITY....... 34
Introduction ................................................................................................................. 34
Fixed-Form Versus Free-Form ............................................................................ 34
Materials and Methods ............................................................................................... 38
Description of the Models .................................................................................... 39
Fixed-form hydrology and transport model: FTLOADDS ............................. 39
Free-form water-quality reactions model: aRSE .......................................... 40
Fusing Fixed- and Free-Form Models ................................................................. 41
Analytical Testing of the FTaRSELOADDS Linkage .......................................... 42
Analytical solution .......................................................................................... 42
Setup for testing of SWIFT2D ....................................................................... 45
Setup for testing of FTaRSELOADDS .......................................................... 47
Results and Discussion .............................................................................................. 47
Benchmarking SWIFT2D ..................................................................................... 47
Verifying FTaRSELOADDS ................................................................................. 48
Conclusions ................................................................................................................ 50
5
3
MODELING HYDROLOGY IN THE SOUTHERN INLAND AND COASTAL
SYSTEMS ................................................................................................................... 58
Introduction ................................................................................................................. 58
Previous Hydrological Modeling of SICS ............................................................ 58
Remodeling the Hydrology of SICS..................................................................... 60
Materials and Methods ............................................................................................... 61
Model Description ................................................................................................ 61
SWIFT2D governing equations ..................................................................... 61
SWIFT2D numerical solution technique ....................................................... 63
SWIFT2D code enhancements and simplifications ..................................... 63
Model Setup ......................................................................................................... 66
Computational domain .................................................................................. 66
Boundary conditions ...................................................................................... 67
Stability considerations ................................................................................. 69
Results and Discussion .............................................................................................. 69
Water-Level Results ............................................................................................. 70
Discharge Results ................................................................................................ 73
Salinity Results ..................................................................................................... 74
Conclusions ................................................................................................................ 75
4
MODELING PHOSPHORUS WATER-QUALITY IN THE SOUTHERN INLAND
AND COASTAL SYSTEMS ...................................................................................... 103
Introduction ............................................................................................................... 103
Materials and Methods ............................................................................................. 105
Boundary Conditions .......................................................................................... 105
Specified water-level boundaries ................................................................ 106
Specified discharge boundaries .................................................................. 107
Atmospheric deposition ............................................................................... 108
Conceptual Models of Water-Quality Processes .............................................. 108
Model 1 ........................................................................................................ 109
Model 2 ........................................................................................................ 110
Model 3 ........................................................................................................ 110
Results and Discussion ............................................................................................ 112
Model 1 ............................................................................................................... 112
Model 2 ............................................................................................................... 112
Model 3 ............................................................................................................... 114
Conclusions .............................................................................................................. 115
5
UNRAVELING MODEL RELEVANCE: THE COMPLEXITY-UNCERTAINTYSENSITIVITY TRILEMMA ........................................................................................ 135
Introduction ............................................................................................................... 135
The Complexity-Uncertainty-Sensitivity Trilemma ............................................ 137
Uncertainty................................................................................................... 138
Sensitivity ..................................................................................................... 139
6
Complexity ................................................................................................... 141
Relevance dilemmas ................................................................................... 143
The relevance trilemma............................................................................... 145
Materials and Methods ............................................................................................. 146
Global Sensitivity and Uncertainty Analysis Methods....................................... 146
Model Description, Application, and Selection of Complexity Levels .............. 149
Model description: TaRSE .......................................................................... 149
Model application......................................................................................... 150
Levels of complexity .................................................................................... 151
Parameterization of Inputs Across Complexity Levels ..................................... 152
Results and Discussion ............................................................................................ 154
Effects of Model Complexity on Sensitivity ....................................................... 154
Morris method .............................................................................................. 154
Extended FAST ........................................................................................... 155
Effects of Model Complexity on Uncertainty ..................................................... 156
Conclusions .............................................................................................................. 160
6
CONCLUDING REMARKS ...................................................................................... 172
Conclusions .............................................................................................................. 172
Limitations ................................................................................................................. 173
Future Research ....................................................................................................... 174
Philosophical Deliberations ...................................................................................... 176
APPENDIX
A
MODEL VERSIONS ................................................................................................. 178
Model and Application Versions: Nomenclature ...................................................... 178
Model and Application Versions: Sub-models ......................................................... 178
B
DETAILS OF THE FTARSELOADDS LINKAGE ..................................................... 182
Section B1 ................................................................................................................. 182
Technical Considerations in the Model Linkage ............................................... 182
Consideration 1: Initial setup of aRSE ........................................................ 183
Consideration 2: Spatially-distributed versus non-spatial .......................... 184
Consideration 3: FORTRAN versus C++ ................................................... 184
Resolution 1: Initial setup of aRSE ............................................................. 186
Resolution 2: Spatially-distributed versus non-spatial ............................... 187
Resolution 3: FORTRAN versus C++ ......................................................... 189
General description of the linkage mechanism .......................................... 189
Section B2 ................................................................................................................. 190
FORTRAN Subroutines for Linkage .................................................................. 190
Module aRSEDIM ........................................................................................ 190
Subroutine READIWQ................................................................................. 191
Subroutine CALLaRSE ............................................................................... 193
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Subroutine aRSE_IN ................................................................................... 195
Subroutine aRSE_OUT ............................................................................... 197
Subroutine RUNaRSE ................................................................................. 198
Subroutine CELLCOUNT ............................................................................ 200
Section B3 ................................................................................................................. 201
READIWQ Input File .......................................................................................... 201
Section B4 ................................................................................................................. 202
Nash-Sutcliffe Calculation for Analytical Testing .............................................. 202
Program STUPOSTPROCESS................................................................... 202
Subroutine POSTPROCESS ...................................................................... 204
Subroutine CORSTAT ................................................................................. 205
C
WATER-QUALITY APPLICATION CODE AND INPUT FILES ............................... 216
Section C1................................................................................................................. 216
Additional Subroutines for Water-Quality Inputs ............................................... 216
Subroutine EDIT_INPUTFILE ..................................................................... 216
Subroutine STRUCTCONCS ...................................................................... 218
Section C2................................................................................................................. 220
Important Input Files for the SICS Water-Quality Simulation ........................... 220
Format for INPUTFLOWCONCS.dat .......................................................... 220
Total Phosphorus Atmospheric Deposition Rates for Model 2......................... 221
Section C3................................................................................................................. 234
XML Input File for Model 3 (XMLINPUT.xml).................................................... 234
IWQ input File for Model 3 (IWQINPUT.iwq) .................................................... 238
SWIFT2D Input File (WETLANDS.inp) for Model 3 .......................................... 239
LIST OF REFERENCES ................................................................................................. 266
BIOGRAPHICAL SKETCH.............................................................................................. 280
8
LIST OF TABLES
page
Table
2-1
Quantities and values used in the comparison of SWIFT2D and
FTaRSELOADDS against the analytical solution ................................................. 51
2-2
Nash-Sutcliffe efficiencies obtained for different methods of integrating aRSE
reactions into FTLOADS ........................................................................................ 52
3-1
Nash-Sutcliffe efficiencies for water-level observation points in SICS ................. 77
3-2
Nash-Sutcliffe statistics for stations in the viciniy of Taylor Slough, stations in
the vicinity of C-111, and all stations in the SICS region. ..................................... 77
4-1
Stations and total phosphorus concentration data used for interpolation of
daily concentrations for specified head boundary conditions in Florida Bay ..... 118
4-2
Data sources and values used for boundary conditions concentrations at the
L-31W discharge source ...................................................................................... 119
4-3
Data sources and values used for boundary conditions concentrations at the
C-111 discharge source. ...................................................................................... 120
4-4
Data sources and values used for boundary conditions concentrations at the
TSB discharge source. ......................................................................................... 121
4-5
Parameters used in the model ............................................................................. 122
4-6
State-variables with initial conditions as used in Model 3 ................................... 123
4-7
Nash-Sutcliffe efficiencies for the water-quality models applied to simulate
total phosphorus in the Southern Inland and Coastal Systems.......................... 124
5-1
Process description for the increasing levels of complexity studied .................. 163
5-2
Probability distributions of model input factors used in the global sensitivity
and uncertainty analysis ...................................................................................... 164
B-1
Explanation of the READIWQ input file structure and read in parameters ........ 201
C-1
Atmospheric deposition rates input to Model 2 ................................................... 221
9
LIST OF FIGURES
page
Figure
1-1
Location of the Southern Inland and Coastal Systems study area ...................... 31
1-2
Reviewed phosphorus water-quality models and algorithms from simple to
complex .................................................................................................................. 32
1-3
Reviewed phosphorus water-quality models and algorithms from
intermediate to complex ......................................................................................... 33
2-1
Schematic detailing the architecture of the code linking the surface-water
model in FTLOADDS with a Reaction Simulation Engine .................................... 52
2-2
Source boundary condition for analytical solution................................................. 53
2-3
SWIFT2D model domain used for comparison of conservative and reactive
transport simulations with analytical solutions ...................................................... 54
2-4
Concentration isolines for 2-D conservative transport from a small
rectangular source as determined by SWIFT2D ................................................... 55
2-5
Concentration isolines for 2-D reactive transport from a small rectangular
source as determined by SWIFT2D ...................................................................... 56
2-6
Spatially-interpolated RMSE and Nash-Sutcliffe efficiencies after 150 minutes
of simulation for the case of transport-reactions-transport-reactions. .................. 57
2-7
Spatially-interpolated RMSE and Nash-Sutcliffe efficiencies after 300
minutes of simulation for the case of transport-reactions-transport-reactions. .... 57
3-1
Location of the Southern Inland and Coastal Systems study area ...................... 78
3-2
Space-staggered grid system showing relative locations of hydrodynamic
characteristics......................................................................................................... 79
3-3
The SICS computational grid, showing the location of Taylor Slough, the
Buttonwood Embankment and the coastal creeks ................................................ 80
3-4
Land-surface elevations. ........................................................................................ 81
3-5
Location of SICS model boundary conditions, including specified water-level
boundaries and discharge sources........................................................................ 82
3-6
Specified hydrologic inputs to SWIFT2D ............................................................... 83
3-7
Water-levels at the six stations in the vicinity of Taylor Slough, simulated with
depth-varying Manning’s n and with constant Manning’s n. ................................. 84
10
3-8
Water-levels at the six stations in the vicinity of C-111, simulated with depthvarying Manning’s n and with constant Manning’s n ............................................ 85
3-9
Water-levels at the six stations in the vicinity of Taylor Slough, simulated with
depth-varying Manning’s n in the current version and the original SICS
application............................................................................................................... 86
3-10
Water-levels at the six stations in the vicinity of C-111, simulated with depthvarying Manning’s n in the current version and the original SICS application ..... 87
3-11
Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained
with SICS v1.2.1, for all 12 water-level stations. ................................................... 88
3-12
Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained
with SICS v1.2.1, for 6 water-level stations in the vicinity of Taylor Slough. ....... 89
3-13
Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained
with SICS v1.2.1, for 6 water-level stations in the vicinity of C-111. .................... 90
3-12
Trends in prediction bias for the 6 stations in the vicinity of Taylor Slough. ........ 91
3-13
Trends in prediction bias for the 6 stations in the vicinity of C-111. ..................... 92
3-14
Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the first four months ..................................................................... 93
3-15
Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the middle four months ................................................................ 94
3-16
Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the final four months..................................................................... 95
3-17
Simulated and measured discharges through five gauged creeks in the
Buttonwood Embankment ...................................................................................... 96
3-18
Rainfall and discharge inputs, and corresponding 2-D discharge vector
distributions for the first four months ..................................................................... 97
3-19
Rainfall and discharge inputs, and corresponding 2-D discharge vector
distributions for the middle four months. ............................................................... 98
3-20
Rainfall and discharge inputs, and corresponding 2-D discharge vector
distributions for the final four months..................................................................... 99
3-21
Rainfall and discharge inputs, and corresponding 2-D salinity distributions for
the first four months ............................................................................................. 100
3-22
Rainfall and discharge inputs, and corresponding 2-D salinity distributions for
the middle four months......................................................................................... 101
11
3-23
Rainfall and discharge inputs, and corresponding 2-D salinity distributions for
the final four months ............................................................................................. 102
4-2
Location of SICS model boundary conditions ..................................................... 126
4-3
Location of water-quality observation points in Florida Bay ............................... 127
4-4
Model 1: Conservative transport assuming deposition and internal sources
are in equilibrium with biotic uptake and internal sinks. ...................................... 128
4-5
Model 2: First-order uptake from the water column using the reactive
transport functionality of SWIFT2D...................................................................... 129
4-6
Model 3: Reactions simulated by aRSE with transport by SWIFT2D................. 130
4-7
Mean proportion of total recovered radioisotope (32P) per mesocosm found in
different ecosystem components over time. ........................................................ 131
4-8
Simulated TP concentrations obtained with Model 1 .......................................... 132
4-9
Simulated TP concentrations obtained with Model 2 .......................................... 133
4-10
Simulated TP concentrations obtained with Model 3 .......................................... 134
5-1
Relevance relative to sources of modeling uncertainty and sensitivity in
relation to model complexity ................................................................................ 165
5-2
Hypothesized trends relating complexity to sensitivity from direct effects,
sensitivity from interactions, and total sensitivity ................................................ 166
5-3
TaRSE application domain, with flow from left to right and bounded above
and below by no-flow boundaries ........................................................................ 166
5-4
Levels of modeling complexity studied to represent phosphorus dynamics in
wetlands................................................................................................................ 167
5-5
Morris method global sensitivity analysis results for surface-water soluble
reactive phosphorus outflow ................................................................................ 168
5-6
Results for sensitivity from direct effects, interactions and output uncertainty .. 169
5-7
Output PDFs for SRP concentration in surface-water outflow ........................... 170
5-8
A suggested framework, employing global sensitivity and uncertainty
analyses................................................................................................................ 171
A-1
SWIFT2D v1.1 comprises the SWIFT2D v1.0 code and additional code from
SICS updates for coastal wetlands...................................................................... 179
12
A-2
FTLOADDS v1.1 comprises the SWIFT2D v1.1. code, leakage code linking
SWIFT2D to SEAWAT, and SEAWAT ................................................................ 179
A-3
SEAWAT comprises the MODFLOW code and the MT3DMS code .................. 179
A-4
FTLOADDS v2.1 comprises SWIFT2D v2.1 and SEAWAT, where SWIFT2D
v2.1 is SWIFT2D v1.1 implemented with integrated leakage ............................. 180
A-5
FTLOADDS v1.2 comprises SWIFT2D v2.2 with updates for TIME but with
the ground-water simulation turned off. ............................................................... 180
A-6
FTLOADDS v2.2 contains SWIFT2D v2.1 linked with SEAWAT and
containing TIME updates. .................................................................................... 181
13
LIST OF ABBREVIATIONS
aRSE
a Reaction Simulation Engine
CERP
Comprehensive Everglades Restoration Plan
eFAST
extended Fourier Amplitude Sensitivity Test
ENP
Everglades National Park
FAST
Fourier Amplitude Sensitivity Test
FDEP
Florida Department of Environmental Protection
FTaRSELOADDS
Flow, Transport and Reaction Simulation Engine in a Linked
Overland-Aquifer Density Dependent System
FTLOADDS
Flow and Transport in a Linked Overland-Aquifer Density
Dependent System
GSA
Global sensitivity analysis
P
Phosphorus
PDF
Probability Distribution Function
SFRSM
South Florida Regional Simulation Model
SFWMD
South Florida Water Management District
SFWMM
South Florida Water Management Model
SICS
Southern Inland and Coastal Systems
SRP
Soluble Reactive Phosphorus
SWIFT2D
Surface-water Integrated Flow and Transport in 2 Dimensions
TaRSE
Transport and Reaction Simulation Engine
TIME
Tides and Inflows in the Mangroves of the Everglades
TP
Total phosphorus
UA
Uncertainty Analysis
USGS
United States Geological Survey
14
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ADAPTIVE SPATIALLY-DISTRIBUTED WATER-QUALITY MODELING: AN
APPLICATION TO MECHANISTICALLY SIMULATE PHOSPHORUS CONDITIONS IN
THE VARIABLE-DENSITY SURFACE-WATERS OF COASTAL EVERGLADES
WETLANDS
By
Stuart John Muller
August 2010
Chair: Rafael Muñoz-Carpena
Major: Agricultural and Biological Engineering
The Everglades region known as the Southern Inland and Coastal Systems is an
important area that supports numerous endangered species and plays a crucial role in
regulating water-quality conditions in Florida Bay. Taylor Slough is a major feature of
this region and represents the primary surface-water pathway for freshwater inputs to
Florida Bay. The slough is also subject to intensive flow management under the
Comprehensive Everglades Restoration Plan, yet the consequences of such
management for water-quality in these oligotrophic and sensitive wetlands are not well
understood. A flexible phosphorus water-quality model was therefore developed and
tested as an exploratory management tool for the region. Complex local hydrodynamics
required that a spatially-distributed hydrodynamic model be used to simulate flow and
transport and the USGS model FTLOADDS was selected for this. A user-definable
biogeochemical reactive component (aRSE) was then coupled with the hydrodynamic
model and the resulting FTaRSELOADDS model was tested against analytical solutions
and field data.
15
Hydrodynamic field testing showed that depth-varying Manning’s resistance was
important for accurately capturing wet and dry conditions during the experimental
period. Conceptual water-quality models of increasing complexity were tested against
experimental phosphorus field data. Results revealed that a simple daily averaging
method was the best approach for atmospheric deposition of phosphorus, which is a
crucial but very uncertain water-quality input. A simple conservative transport model
provided the best fit between modeled and total phosphorus concentration data. Similar
results were also obtained with a more complex and mechanistically justifiable waterquality model. The adaptability of the biogeochemical component was used to study
how additional model complexity affects model uncertainty, sensitivity and relevance by
evaluating progressively more complex conceptual models using global sensitivity and
uncertainty analyses. The framework applying these methods is suggested as a useful
way of evaluating models in general, and deciding upon a relevant model structure
when the freedom to dictate complexity exists.
16
CHAPTER 1
INTRODUCTION
The Southern Inland and Coastal Systems of the Everglades: A Region at Risk
The Southern Inland and Coastal Systems (SICS) region of the southern
Everglades (Figure 1-1) connects Taylor Slough and the C-111 marl prairie wetlands
with Florida Bay, and represents an important region of Everglades study and
management (SFWMD and FDEP, 2004; CRGEE and NRC, 2002). Though Taylor
Slough is substantially smaller than Shark River Slough, in both discharge and areal
extent, it plays an important role in regulating water-quality in Florida Bay (Fourqurean
and Robblee, 1999). Additionally, the region encompasses thousands of acres of
habitat that support dwindling populations of saltwater and freshwater animal species
(van Lent et al., 1998), fifteen of which are listed as threatened or endangered with
extinction (Beccue, 1999), including the Federally protected Cape Sable Seaside
Sparrow (Pimm et al., 2004).
Flow through the southern Everglades has been increased as part of the
Comprehensive Everglades Restoration Plan (CERP), with further increases imminent.
The potential effects of these changes on nutrient conditions in Taylor Slough, the
neighboring wet marl prairies, or the estuaries of Florida Bay is not well understood and
the subject of ongoing research (Childers, 2006). Studies suggest that the SICS area is
already under intense ecological stress from past management decisions that have
impacted flow and nutrient conditions (Childers, 2006; Gaiser et al., 2006; Armentano et
al., 2006). In addition, gradual reductions in freshwater inputs flowing southwards have
contributed to the encroachment of saltwater tolerant species, primarily mangrove
forest, into previously freshwater marsh vegetation (Smith, 1998). Of particular concern
17
are the possible consequences of additional nutrient loading to Florida Bay (SFWMD
and FDEP, 2004), which has seen an increase in the incidence of harmful algal blooms
and mass seagrass die-off (Fourqurean and Robblee, 1999).
The Everglades are a highly oligotrophic system (Noe et al., 2001) due to a natural
scarcity in bioavailable phosphorus. The concentration of phosphorus in the surfacewater is therefore a principal consideration in the Everglades restoration. Freshwater
marshes in the SICS region are characterized by unique macrophyte and periphyton
communities that are adapted to phosphorus-scarce conditions. Periphyton taxa have
been shown to be very sensitive to phosphorus conditions (Gaiser et al., 2004), with
cascading ecological consequences resulting from even low levels of nutrient
enrichment (Gaiser et al., 2005). Additionally, the low phosphorus loading with
freshwater inputs to the estuaries of Florida Bay means that water from the Gulf of
Mexico is their most important source of phosphorus, as opposed to the upstream
watershed as is normally the case (Chen and Twilley, 1999; Fourqurean et al., 1992).
This reversal in the source of the limiting nutrient, compared with typical estuaries
(biogeochemically speaking), is the reason they are referred to as “upside-down”
estuaries (Childers, 2006). It is believed that phytoplankton and seagrasses in eastern
Florida Bay, which is most isolated from the Gulf of Mexico, are therefore phosphoruslimited (Fourqurean et al., 1992). Higher natural or anthropogenic loadings of
phosphorus that may accompany increasing freshwater inputs could potentially increase
the frequency, intensity, and duration of phytoplankton blooms in regions of Florida Bay.
However, significant increases in the volume of freshwater inflow relative to the
nutrient additions from upstream sources could make terrestrial phosphorus inputs
18
negligible, and may possibly even suppress the natural marine phosphorus supply by
dilution. Recent research has shown that freshwater inflows have been found to
enhance oligotrophy where Taylor Slough sufficiently flushes the area and suppresses
the intrusion of water from Florida Bay (Childers, 2006). As such, any increase in
freshwater inflows could enhance oligotrophic conditions in the ecotone between fresh
and marine waters, especially during the wet season.
Time-series water-quality and soil phosphorus data shows a general pattern of low
phosphorus availability along Taylor Slough during the wet season except near the
marine source (Boyer et al., 1999), and the influence of marine phosphorus moving
upstream during the low-flow dry season. This was not expected for the southern
Everglades ecotone as light easily penetrates the clear shallow waters above seagrass
pastures, which are known to efficiently sequester marine phosphorus (Fourqurean and
Robblee, 1999). New research in the area has indicated that surface-water phosphorus
concentrations were unexpectedly high in the Taylor Slough ecotone during the dry
season (Childers, 2006). It is conjectured that relatively phosphorus-rich ground-water
inputs to this ecotone are significant during the dry season, when surface-water
hydraulic heads are lowest and residence times are long enough to deplete dissolved
organic matter, thus reducing productivity and phosphorus consumption (Price et al.,
2006; Childers, 2006). Strong interactions between ground-water and surface-water in
this region mean that increased surface-water heads may impact this ground-water
exchange, and thereby affect phosphorus conditions.
19
Opportunities for Spatially-Distributed Mechanistic Modeling of Phosphorus in
SICS
A model of spatially-distributed surface-water phosphorus conditions for the region
is required to study these issues. Spatially-distributed mechanistic modeling of wetland
water-quality remains a challenging field of hydrology. Modeling the movement of
solutes both within and with the water is contingent upon reliable flow modeling, which
is a difficult task unto itself in the vegetated and hydrodynamically complex SICS
wetlands (Swain et al., 2004; Langevin et al., 2005). In addition, water-quality
constituents are subject to a multitude of chemical, physical and biological processes in
wetlands where unique biogeochemistry and ecology are drivers of, as much as driven
by, water-quality.
Hydrologic Modeling of SICS
Numerical models for simulating water flow south of Lake Okeechobee have been
developed for three distinct regions. The South Florida Water Management Model
(SFWMM) (SFWMD, 2005) and its successor, the South Florida Regional Simulation
Model (SFRSM) (Lal et al., 2005), simulate the highly managed hydrology between
Lake Okeechobee and Everglades National Park (ENP). The southern and western
offshore waters of Florida Bay are modeled with the Florida Bay Hydrodynamic Model
(Hamrick and Moustafa, 2003). The hydrologically complex region between these
models’ domains is encompassed by SICS, and is characterized by surfacewater/ground-water and freshwater/saltwater interactions within a highly vegetated and
hydrodynamically unsteady environment. A further specialized modeling effort was
therefore required (Swain et al., 2004; Langevin et al., 2005; Wang et al., 2007), which
culminated in the Flow and Transport in a Linked Overland-Aquifer Density Dependent
20
System (FTLOADDS) model (Langevin et al., 2005). FTLOADDS links the managed
hydrology of the mainland with that of Florida Bay; outputs from SFWMM are applied as
boundary conditions in FTLOADDS, the outputs from which are in turn applied as
boundary conditions for the Florida Bay Hydrodynamic Model. In this way, an integrated
hydrologic modeling framework of the region was produced that could propagate the
hydrologic consequences of upstream management scenarios onto the downstream
systems. Furthermore, detailed hydrologic conditions can be simulated for use by
mechanistic ecological models that rely on such information, and which is typically not
practically obtainable at the desired resolution (Swain et al., 2004).
FTLOADDS is itself composed of two models; the Surface-Water Integrated Flow
and Transport in Two Dimensions (SWIFT2D) model (Schaffranek, 2004) adapted for
coastal wetlands (Swain, 2005), and the variable-density ground-water model SEAWAT
(Langevin and Guo, 2006). An application of FTLOADDS to the SICS area that uses
only SWIFT2D, and thus neglects surface-water/ground-water interactions, has been
shown to provide acceptable hydrodynamic results (Swain et al., 2004).
Water-Quality Modeling of SICS
Models of the Everglades hydrology and hydrodynamics have and continue to be
addressed, but analogous tools for water-quality are still needed (McPherson and
Torres, 2006). One approach to addressing this need is to develop a detailed
ecosystem model (Wang and Mitsch, 2000). This approach simulates a large number
of biogeochemical processes and therefore requires many parameters, which make the
model cumbersome to apply and prone to overparameterization (Beven, 2006a). Such
conceptually complex models often use free-form tools such as STELLA (Doerr, 1996),
which can be readily tailored to the specific water-quality considerations at hand.
21
However, the versatility often comes at the expense of spatial heterogeneity, which is
an untenable simplification in the context of the scale and spatial complexity of SICS.
For instance, the spatial variation in microtopography, landcover, and complex
flow boundaries that include canals, pumping stations, and tidal effects, are known to be
important factors that determine water-level (and therefore whether conditions are wet
or dry) and velocity in SICS (Swain et al., 2004). Flow velocity is crucial for accurate
solute transport when using the advection-dispersion equation. Water-level is
biogeochemically important because it determines whether conditions are dry or wet,
which has implications for the presence or absence of aquatic biota and senescence
and decomposition processes (Reddy et al., 1999). Both velocity and water-level are
important for accurate estimation of discharge, which with concentration determines
loading rates that would be of interest to Florida Bay. Additionally, the original SICS
hydrodynamic modeling effort demonstrated the striking effect of wind shear on waterlevels and the directionality of discharges through coastal creeks, and in turn, important
wind-driven mixing (Swain et al., 2004). In order to accurately capture these transient
effects in the transport solution a mechanistic hydrodynamic model is required that
accounts for their effects. Consequently, a spatially-distributed and mechanistic
hydrodynamic foundation was considered requisite.
A more common and simplified approach is to aggregate all phosphorus cycling
mechanisms into a single lumped process that captures net uptake or release (Kadlec
and Knight, 1996; Mitsch et al., 1995; Walker, 1995), or some combination of lumping
and mechanistic methods (Kadlec, 1997). This simplification in biogeochemistry is
counterbalanced by the complexity of spatial heterogeneity in hydrology. However, the
22
modeling efforts cited simulated surface-water flow using simplified mass balance
approaches (Walker, 1995; Wang and Mitsch, 2000) or as nondispersive, unidirectional
plug flow (Kadlec, 1997), which are not suitable for the complex conditions in SICS. In
addition to homogeneous hydrology, there is also no accounting for spatial
heterogeneity in wetland components and processes that may be important or desirable
(for example, soil phosphorus concentration or accretion and macrophyte or periphyton
biomass).
With the arrival of spatially-distributed mechanistic models of Everglades
hydrology, the logical step to develop a mechanistic water-quality model that built on
this foundation was undertaken. The result was TaRSE, the Transport and Reaction
Simulation Engine (Muller and Muñoz-Carpena, 2005; Jawitz et al., 2008; James et al.,
2009). The term “reaction simulation engine” alludes to a novel characteristic of
TaRSE; the state-variables and equations relating them are user-defined. To our
knowledge, this was the first time a spatially-distributed mechanistic water-quality model
had been developed with the built-in flexibility of a free-form simulation model for
defining the system of biogeochemical water-quality processes. This pairing represents
an important new management and research tool for the SFWMD to address
phosphorus related water-quality issues. Though originally integrated into SFRSM, a
version of TaRSE without the transport (now a Reaction Simulation Engine - aRSE) has
subsequently been extricated from SFRSM and modularized.
Model Selection
A critical consideration in the selection of a model is the choice of appropriate
complexity. In the context of mechanistic water-quality modeling, which entails a twostep process of simulating hydrology and biogeochemistry, this choice must be made
23
twice. Historically, the complexity of each of these components has often been mutually
exclusive, though the greater prevalence of spatial data and computational power have
seen a move towards models with complex treatments of both hydrology and
biogeochemistry (Costanza et al., 1990). Figures 1-2 and 1-3 present a number of
phosphorus water-quality models that were reviewed and classified according to their
overall complexity. They demonstrate the wide range of complexities and approaches
that exist for modeling phosphorus-related water-quality.
A distinguishing feature in the design of models that is associated with their
complexity is whether they are “fixed-form” (usable as-is only), or “free-form”
(intentionally user-definable). The fixed-form development paradigm is generally
applied for complex spatially-distributed models (of which hydrologic models are a prime
example), which require computationally efficient numerical solutions. Many hydrologic
models are based on fundamental laws of physics, and consequently are quite versatile
despite their rigid design. Free-form models are sometimes referred to as dynamic
systems models, and are more suitable to simulating systems where spatial
heterogeneity can be neglected. The relatively light computational demands of a
spatially-lumped model compared with a spatially-distributed one make it amenable to a
more flexible design. The user is therefore able to specify state-variables of interest and
how they are related, with the result that such tools are highly adaptable to a variety of
system applications, including biogeochemical cycling. The extensive and varied
application of STELLA, a widely used example of a free-from model, is indicative of this
versatility (Doerr, 1996).
24
The complexity of SICS hydrology calls for a fixed-form spatially-distributed
mechanistic hydrodynamic model. Yet the lack of a clear indication of what, exactly, a
phosphorus water-quality model should look like (Figures 1-2 and 1-3), and the looming
need for models of other water-quality constituents and ecological components, calls for
a free-form solution. It was therefore proposed that a fusion of the fixed-form and freeform development paradigms be attempted by linking the SWIFT2D model within
FTLOADDS with aRSE.
Important SICS Modeling Considerations
Since the initial application of SWIFT2D to SICS (Swain et al., 2004) the model
has been further adapted for application to the larger Tides and Inflows to the
Mangroves of the Everglades (TIME) domain (Wang et al., 2007), which includes the
SICS model domain but is applied using a somewhat larger cell size (500 m as opposed
to 304.8 m). These changes include a number of potentially important simplifications;
rainfall and evapotranspiration (ET) rates are now applied homogenously, and the
Manning’s coefficient no longer varies with flow-depth, though it is now treated
anisotropically where before it was considered isotropic. The implications of the
changes to rainfall and evapotranspiration have been sufficiently justified for SICS
(Wang et al., 2007). The consequences of depth-invariant Manning’s coefficients are
unclear though, particularly since this proved to be an important factor in the original
SICS hydrologic modeling effort (Swain et al., 2004). Depth-varying Manning’s n was
also found to be important under similar assumptions of homogeneous rainfall and ET in
the ridge and slough Everglades landscape (Min et al., 2010). Of particular concern is
how this change affects the ability of SWIFT2D to accurately capture dry versus wet
conditions, which are important for phosphorus cycling (Reddy et al., 1999).
25
A second important consideration pertain to atmospheric deposition of total
phosphorus (TP). This is a crucial input for modeling water-quality under the
oligotrophic conditions found in SICS (Sutula et al., 2001; Noe and Childers, 2007).
However, atmospheric deposition of phosphorus is notoriously difficult to quantify due to
persistent sample contamination and limitations in the sampling methods (Redfield,
1998; Ahn, 1999). Bulk phosphorus deposition in Florida is estimated to be comprised
of as much as 30-50% dry deposition from resuspended agricultural soils,
phosphogypsum mining, urban emissions and transported dust (Landing, 1997; Meyers
and Lindberg, 1997). However, rainfall is known to scavenge aerosol phosphorus and
incorporate dry deposition into wet deposition estimates, further complicating
quantification of the process.
Measured rates of bulk atmospheric deposition in the Everglades exhibit great
variability, ranging from 0.017 to 0.07 g TP/m2/yr, with an average of 0.03 g TP/m2/yr
(Sutula et al., 2001). Fitz and Sklar (1999) estimated total phosphorus deposition to be
0.03 g TP/m2/yr for the Everglades, which is similar to an estimate by Davis (1994) of
0.036 g TP/m2/y, and the same as that of 0.03 g TP/m2/yr found for the Kissimmee
region 100 miles north of the Everglades (Moustafa et al.. 1996). Rates as low as
0.0006 g P/m2/yr have been estimated for the Bahamas (Graham and Duce, 1982).
South Florida weather is characterized by frequent convection thunderstorms, which
can scavenge aerosol phosphorus from the upper atmosphere (Poleman et al., 1995),
and the location of SICS in the proximity of Miami could subject it to higher deposition
rates associated with adjacent urban or industrial areas (Paerl, 1995; Redfield, 1998).
26
Consequently, there is great uncertainty in the quantification of atmospheric
deposition of phosphorus, and the process will therefore represent a major source of
uncertainty in any phosphorus water-quality modeling effort. How best to input this
source remains an open question. Another important open question is, given the freeform of aRSE, what complexity of water-quality model to select. This raises the issue of
how to balance model complexity and relevance.
Model Relevance
A principal tenet of model development is the establishment of relevance (Zadeh,
1973). Relevance is determined by balancing the complexity of a model against its
uncertainty, given the modeling objectives at hand. This topic is introduced and
discussed in great detail in Chapter 5, which is presented as a standalone paper, but is
briefly reviewed here to clarify the motivation.
Model complexity is a property of the degree of detail implicit to the conceptualized
rendition of reality, including the number of state variables and processes simulated.
Increasing complexity implies ever more variables and processes, and therefore ever
fewer simplifying assumptions. This results in a modeled version of reality with greater
mechanistic integrity and thus less structural uncertainty. However, each new statevariable and process introduced requires additional calibration and parameterization
data, all of which are subject to some measurement uncertainty. These measurement
uncertainties accumulate and eventually outweigh any reductions in structural
uncertainty gained by increasing complexity (Hanna, 1988). The sensitivity of model
outputs also accumulates with consequences for the practicability of the model
(Snowling and Kramer, 2001). Each added process that exerts some influence over a
state-variable, either directly or through interactions with other processes, represents
27
additional flexibility in the model that can lead to overparameterization issues that can
seriously undermine the validity of a model (Beven and Binley, 1992).
Two model evaluation methods exist that are ideally suited to elucidating these
relationships. Uncertainty analysis applies Monte Carlo simulations to propagate the
uncertainty inherent to model inputs onto outputs of interest. In this way, the
uncertainties in an output for a given model structure, and subject to the given model
input requirements, can be assessed and compared. Global sensitivity analyses
determine where the uncertainty in an output originates from (Saltelli et al., 2000).
Together, these evaluation methods can shed light on how much uncertainty is in the
model, and why it is there (Muñoz-Carpena et al., 2007). When performed in the
context of varying model complexity we are then able study how additional complexity
affects the model’s inner workings (Jawitz et al., 2008).
The process of defining a model is also the process of defining a model’s
complexity; the ultimate source to which many modeling considerations and challenges
can be traced. This tripartite web of interacting complexity, uncertainty, and sensitivity
has not been well-studied in very complex models (Lindenschmidt, 2006)precisely
because they have typically been fixed-form. A flexible model structure presents a novel
opportunity to subtly experiment with advanced levels of model complexity and to
assess how complexity affects uncertainty, sensitivity, and ultimately relevance.
Research Questions and Objectives
Research Questions
There is urgent need for modeling tools to simulate a variety of water-quality
issues of interest in the southern Everglades, and in particular phosphorus conditions in
the sensitive of oligotrophic freshwater marshes. Assessing likely phosphorus
28
conditions in the surface-water in response to CERP flow management decisions is a
pressing concern. Though a suitable hydrodynamic model of SICS has been identified
and tested for hydrological outputs (Swain et al., 2004), its suitability to supporting
spatially-distributed water-quality simulations needs to be assessed. Furthermore, as
indicated atmospheric deposition of phosphorus is an important process in the
oligotrophic freshwater Everglades that remains very difficult to quantify. How best to
handle this crucial input is therefore a major source of uncertainty. Finally, with the
flexibility of a free-form water-quality model the definition of the phosphorus conceptual
model becomes a moving target, yet a suitable complexity must eventually be settled
upon. Open questions to be addressed in this dissertation include:
•
What are the consequences of recent changes to the SWIFT2D code that
included removal of depth-varying Manning’s roughness? In particular, how do
these changes affect the hydrodynamic prediction of wet versus dry conditions in
SICS, which are important distinctions for a water-quality simulation?
•
Given the acknowledged uncertainty associated with quantifying atmospheric
deposition of phosphorus, what methods of inputting this source to the waterquality model produce the most accurate simulated concentrations?
•
What is the simplest phosphorus water-quality model that would produce
acceptable results for SICS? Can a more complex and mechanistic model of
water-quality produce comparable or better results than a simpler one?
•
Given the tradeoffs between complexity and uncertainty, how does one choose
what model complexity is appropriate, and how does uncertainty and sensitivity
change with the addition of further complexity?
Objectives
1. Development of a combined fixed-form/free-form spatially-distributed hydrologic and
biogeochemical model, validated against analytical testing, which is suitable for
application to simulate phosphorus water-quality in SICS (Chapter 2).
2. Application of the new tool to study the importance of depth-varying Manning’s
roughness in hydrodynamic simulations of SICS surface-water (Chapter 3).
29
3. Application of the new tool to determine how best to input phosphorus additions by
atmospheric deposition, and to determine what complexity of phosphorus waterquality model best captures measured phosphorus conditions in SICS surfacewaters (Chapter 4).
4. Formal evaluation of the effect of using different complexity biogeochemical
conceptual models on output uncertainty, global sensitivity, and model relevance
(Chapter 5).
30
Figure 1-1. Location of the Southern Inland and Coastal Systems study area (from
Swain et al., 2004).
31
Figure 1-2. Reviewed phosphorus water-quality models and algorithms (from simple to
complex from left to right).
32
Figure 1-3. Reviewed phosphorus water-quality models and algorithms (from
intermediate to complex from left to right).
33
CHAPTER 2
FUSION OF FIXED-FORM AND FREE-FORM MODELS FOR ADAPTIVE
SIMULATION OF SPATIALLY-DISTRIBUTED WETLAND WATER-QUALITY
Introduction
Spatially-distributed mechanistic water-quality modeling of wetlands, such as
those in southern Florida, requires simulating three distinct, yet inter-related, aspects: 1)
the quantity and timing of water distribution (“hydrodynamics”); 2) the motion of
constituents with and within the water by advection, dispersion and diffusion
(“transport”); and 3) local biogeochemical processes that change the nature or state of
constituents (“reactions”). Mechanistic hydrodynamics and transport of large-scale
wetland systems generally requires spatially-distributed modeling. The numerical
considerations associated with this, in conjunction with the generality of the underlying
physics, results in models that are hard-coded – or “fixed-form” – with little or no
freedom on the part of the user to influence the theoretical concepts driving the
simulation. By contrast, biogeochemical reactions can be more readily conceptualized
as a non-spatial system by relying on hydrodynamics and transport to provide the
spatial connection. Water-quality reactions are therefore more amenable to non-spatial
dynamic systems simulation, for which user-definable – or “free-form” – modeling tools
are regularly used. The need for spatially-distributed mechanistic water-quality models
therefore offers an excellent opportunity to integrate the versatility of a “free-form”
dynamic systems model with the mechanistic and numerical rigor of a spatiallydistributed fixed-form modeling.
Fixed-Form Versus Free-Form
Truly mechanistic models of hydrology apply theoretically derived equations of
flow dynamics, which are generally well-understood and are based on uniformly
34
applicable laws of physics. For instance, the Surface-Water Integrated Flow and
Transport in Two Dimensions (SWIFT2D) model (Leendertse, 1987; Schaffranek, 2004;
Swain, 2005) applies the St. Venant equations, which are derived from Newton’s
Second Law (Conservation of Momentum) and the Principle of Conservation of Mass.
Spatial discretization of the model domain is necessary to capture variability in space,
and transience is captured by repeatedly solving the equations in successive timesteps. This approach is contingent on limitations to the size of both spatial and temporal
discretizations in order to maintain mathematical stability of the numerical solutions.
Stability considerations in conjunction with simulations of large areas or long periods
can therefore become computationally intensive, even limiting, despite the modern
computational capacities we have at our disposal.
To ensure numerical efficiency such hydrologic models are generally hard-coded
into a fixed-form. This limits the model’s application to only those conditions that meet
the underlying (and fixed) assumptions. However, given the universality of physics,
mechanistic flow models that use equations derived from theoretical principles remain
generally versatile. For example, SWIFT2D has been applied to a multitude of water
bodies and locations, including: Jamaica Bay, New York (Leenderste, 1972), the Dutch
Delta Works of the Netherlands (Dronkers et al., 1981; Leendertse et al., 1981), the
Dutch Wadden Sea (with modifications to evaluate mixing) (Riddererinkhof and
Zimmerman, 1992), the Eastern Scheldt estuary in the Netherlands (Leendertse, 1988),
the Pamlico (Bales and Robbins, 1995) and Neuse River (Robbins and Bales, 1995)
estuaries of North Carolina, Tampa Bay (Goodwin, 1987), Hillsborough Bay (Goodwin,
1991), and the upper Potomac estuary in Maryland (Schaffranek, 1986).
35
Transport of dissolved and suspended constituents can be mechanistically
simulated with the theoretically derived advection-dispersion equation (Equation 2-1). A
reaction term can be introduced (now the advection-dispersion-reaction equation) to
simulate first-order growth or decay reactions. Given the dependence on velocity,
transport modeling within spatially-distributed systems is often integrated into existing
hydrologic models, and inherits a fixed-form structure. This is the case for both
SWIFT2D (Schaffranek, 2004) and SEAWAT (Langevin and Guo, 2006). However, the
underlying simple and generic mathematical formulation of linear growth and decay
kinetics make the reactive transport universally applicable for any constituent, provided
first-order reaction kinetics are appropriate for the process.
The introduction of biogeochemical processes, which are fundamental to wetland
water-quality (Mitsch and Gosselink, 2000), greatly complicates matters because such
processes are too complex to be mechanistically derived from a physics-based
foundation. The biology, chemistry and physics of the aquatic environment all interact to
form a byzantine web of feedbacks that constitute some of the most complex natural
systems science has endeavored to conceptualize. Simulating such complex
biogeochemical systems requires substantial simplification and abstraction, and even
then presents a significant technical challenge (Arhonditsis and Brett, 2004).
Matters are further confounded by the sheer variety of water-quality subjects –
sediments, nutrients, pesticides, bacteria, pH, salinity, dissolved oxygen, dissolved
organic matter, and algae, to name but a few – each of which are involved in their own
unique biogeochemical processes. Spatially-distributed modeling of water-quality issues
has therefore also generally been of the fixed form. Particular water-quality functionality
36
is to address a particular water-quality issue hard-coded into a given hydrologic model,
which limits the applicability of the water-quality model to the range of appropriate
hydrologic applications, and limits the conceptual model of the water-quality constituent
to the hard-coded form.
Rarely have the power of free-form dynamic system models and fixed-form
spatially-distributed hydrologic models been integrated. The aforementioned
development of TaRSE (Jawitz, et al., 2008; James et al., 2009) in Chapter 1 was, to
the best of our knowledge, the first instance of this. The reasons for this are unclear,
although it is sufficiently intriguing to warrant some conjecture. Dynamic simulation
models have generally been written in object-oriented programming languages since
these are conceptually well matched to the task. By comparison, spatially-distributed
mechanistic models have been written in linear programming languages such as
FORTRAN, which carry benefits for numerically efficient processing of the large arrays
of data associated with a spatially discretized domain.
Many of the most popular hydrologic models have their foundations in the early
days of hydrologic model development, when the fusion of linear and object-oriented
programming philosophies was uncommon because computational limitations of the day
demanded the highest possible efficiencies. More often than not this meant coding in
FORTRAN. The two sub- models of FTLOADDS, both coded in FORTRAN, are classic
examples of this: SIMSYS2D (Leendertse et al., 1987) is based on model development
from the 1970s (Leendertse, 1970) and is the progenitor of SWIFT2D; and SEAWAT is
ultimately an adapted version of a 1983 modular ground-water model that would
become MODFLOW (McDonald and Harbaugh, 1988). Mixed-language programming
37
has become increasingly common with ever-growing computational capacity
(Zimmermann et al., 1992; Cary et al., 1997). Although languages such as FORTRAN
still offer the greatest control over computational efficiency, many higher-level
programming and even scripting languages are becoming popular alternatives for
applications that are not critically limited by computational considerations (Oliphant,
2007).
It is also the case that model development is never without a purpose, and it is
difficult to conceive of developing a water-quality model without a particular waterquality issue as the objective. In hindsight, it seems that a combination of serendipity
and naïveté was at play in the development of TaRSE. The lack of experience at the
time in both biogeochemistry and water-quality modeling on the part of this author, who
was tasked with researching and formulating the preliminary water-quality
conceptualization (Muller and Muñoz-Carpena, 2005), lead to particular attention and
frustration associated with the choice of model complexity. This was amplified by the
express intention of the project to develop a tool for application to water bodies
throughout the Everglades, including wetlands, canals, and reservoirs, all of which are
subject to their own biogeochemical idiosyncrasies (Reddy et al., 1999). It would
appear that these factors combined with the object-oriented programming paradigm
brought to the project by the team programmer to inspire the notion of a truly free-form
spatially-distributed water-quality model.
Materials and Methods
In this section we describe the models selected for linkage and the processes by
which their integration was achieved. Following this we present the results of testing
conducted to validate the reactive transport of the fixed-form model against known
38
analytical solutions. Validation of the linkage between the fixed- and free-form models
is then presented.
Description of the Models
The fixed-form hydrologic model used was Flow and Transport in a Linked
Overland-Aquifer Density Dependent System (FTLOADDS) (Wang et al., 2007), and the
free-from water-quality model was a Reaction Simulation Engine (aRSE) (Jawitz, et al.,
2008). Together, they constitute a novel and potentially powerful new water-quality
modeling tool for the coastal Everglades wetlands; Flow, Transport and a Reaction
Simulation Engine in a Linked Overland-Aquifer Density Dependent System
(FTaRSELOADDS).
Fixed-form hydrology and transport model: FTLOADDS
The USGS has recently developed FTLOADDS as a tool for simulating linked
surface and subsurface hydrology and transport. Surface hydrology in FTLOADDS is
modeled using the Surface-water Integrated Flow and Transport in Two Dimensions
(SWIFT2D) model (Swain, 2005), which simulates vertically-averaged, variable-density,
transient overland flow and transport of solutes. Subsurface hydrology in FTLOADDS is
modeled using SEAWAT (Langevin, 2001; Guo and Langevin, 2002; Langevin and Guo,
2006), which simulates three-dimensional, variable-density, transient ground-water flow
and transport through a porous media. The two models are linked through the
exchange of water and constituent mass between the surface and subsurface (Langevin
et al., 2005).
A number of different versions and implementations of FTLOADDS, SWIFT2D
within FTLOADDS, and the SICS application using these tools are referred to.
Appendix A contains a detailed breakdown of the distinguishing features of each version
39
and the nomenclature adopted by the USGS, and adapted herein. In this chapter,
reference to “FTLOADDS” will imply FTLOADDS v1.2, which implements the latest
SWIFT2D code used in FTLOADDS v2.2 (Wang et al., 2007) but with leakage and
ground-water flow disabled, hence FTLOADDS v1.2 and SWIFT2D v1.2 (see Appendix
A). In Chapter 3 some code changes were implemented that constituted a new subversion, v1.2.1. Each version of each model is graphically outlined in Appendix A to
facilitate clarification of the sub-models that comprise each model and application
version.
Free-form water-quality reactions model: aRSE
With support from SFWMD and USGS, a group at UF recently developed a
biogeochemical component, the Transport and Reaction Simulation Engine (TaRSE),
for simulating the water-quality processes that control phosphorus concentrations and
fate in Everglades wetlands (Jawitz et al., 2008; James et al., 2009). The term
“simulation engine” alludes to the generic nature of the tool, which permits the user to
define the conceptual biogeochemical system by controlling both the state-variables and
the mathematical form of the processes that connect them. Given the existence of a
number of proven hydrologic models for the Everglades, TaRSE was developed as a
water-quality module, and therefore relies on a suitable hydrologic model to simulate
flow and provide the necessary hydrodynamic inputs. The South Florida Regional
Simulation Model (SFRSM) was selected as the first such hydrologic model. However,
the absence of any solute transport functionality in SFRSM necessitated this be
incorporated into the development of TaRSE. This transport functionality is contingent
on the triangular mesh geometry employed by SFRSM for spatial discretization, which
became a significant restriction on the portability of TaRSE for use by other hydrologic
40
models, many of which already have transport functionality of their own and a square
spatial discretization geometry. The modularity of TaRSE was therefore re-established
by extricating it from SFRSM and removing the transport functionality, leaving it as
simply a Reaction Simulation Engine (aRSE). Portability of aRSE was finalized through
its modularization into a dynamically linked library (DLL), which is callable by any model,
hydrologic or otherwise, to which it offers a powerful and flexible simulation engine.
Fusing Fixed- and Free-Form Models
Figure 2-1 presents a schematic of the linkage implemented to integrate
FTLOADDS and aRSE. Blue portions correspond to FTLOADDS code, green to aRSE
code, and yellow to the linkage code. Black text and lines indicate FORTRAN, red text
and lines indicate C++, solid lines indicate models, dashed lines indicate subroutines,
solid line arrows indicate calls to subroutines in the same language, and mixed-dash
arrows indicate calls from one language to another.
Full details of the technical considerations in the linkage are presented in
Appendix A, but are briefly reviewed here in reference to Figure 2-1:
•
An additional method for inputting aRSE parameters and state-variables was
required for this information to be available to FTLOADDS at the beginning of the
simulation. This was important for correctly exchanging hydrodynamic
information between the models, and is achieved through a new input file that is
read by the READIWQ subroutine during setup of SWIFT2D.
•
FTLOADDS and its sub-models are all coded in FORTRAN, whereas aRSE is
coded in C++. Mixed-language programming methods were therefore required to
facilitate communication between the two models (indicated by the color-coding
and mixed-dash lines in Figure 2-1).
•
Since aRSE computes water-quality reactions for one cell at a time, it was
necessary to establish a framework that would efficiently repeat this process for
each of the cells in the spatially-distributed hydrodynamic domain. A temporary
storage array is used to hold the latest values required by aRSE for each cell,
which are in turn overwritten after each cell is processed by aRSE and returned
to FTLOADDS once all cells have been reacted.
41
The general functionality of the linkage is described in detail in Appendix B
(Section B1). The code comprising the various subroutines of the linkage is given in
Appendix B (Section B2). An explanation of the IWQ input file is given in Appendix B
(Section B3).
Analytical Testing of the FTaRSELOADDS Linkage
In order to verify that the code used to integrate FTLOADDS and aRSE was valid,
a series of comparisons between numerically modeled results and known analytical
solutions were conducted. While TaRSE has been previously tested, no published
analysis of aRSE exists. Similarly, though widely used and thoroughly tested in
practice, no published comparison of SWIFT2D reactive transport against known
analytical solutions were identified. Therefore, the procedure outlined was intended to
test both models in addition to their linkage. This process consisted of two main steps:
1) testing the reactive transport of SWIFT2D against an established analytical solution;
and 2) reproducing these results using aRSE to perform the reactions calculations
previously performed by SWIFT2D. In this way, the SWIFT2D code was verified
against an analytical solution and could be used as a benchmark against which to verify
the linkage. If FTaRSELOADDS reproduced the same results by relying on SWIFT2D
for transport and the linked code of aRSE for the reactions, then both the linkage and
the reactions code of aRSE will have been validated since a failure of either would
preclude matching results.
Analytical solution
Reactive transport of dissolved constituents in two dimensions is described
according to the advection-dispersion-reaction (ADR) equation (Equation 2-1):
42
∂C
∂C
∂C
∂ 2C
∂ 2C
= −v x
− vy
+ Dx
+
− kr C
D
y
∂t
∂t
∂t
∂x 2
∂y 2
(2-1)
where C is concentration of the solute of interest; t is time; x is distance in the xdirection; y is distance in the y-direction; vx is local velocity in the x-direction; vy is local
velocity in the y-direction; Dx is effective dispersion in the x-direction; Dy is effective
dispersion in the y-direction; and kr is the solute reaction rate.
The controlled velocity conditions implemented in SWIFT2D to ensure uniform
velocity throughout the domain required using a type-three (flux-averaged)
concentration boundary condition. Leij and Bradford (1994) present a suitable analytical
solution for third-type boundary conditions in three dimensions, with a rectangular
source area (Figure 2-2) of width a (in the y-direction), height b (in the z-direction), and
flow in the x-direction, and provide the 3DADE software for numerically solving the
solution. This software is now available as part of the STANMOD suite of numerical
tools (Simunek et al., 1999; available at http://www.pcprogress.com/en/Default.aspx?stanmod) for solving various analytical solutions to the
ADR equation.
In order to implement the 3-D solution for the horizontal 2-D conditions that
SWIFT2D simulates, the x-direction was oriented in the direction of horizontal
longitudinal flow, the y-direction as horizontally transverse to the direction of flow, and zdirection as the vertical plane over which the depth-averaged Navier-Stokes equations
are integrated. In such an orientation vertically integrated conditions can be
approximated by setting b sufficiently large compared with the dimension a to produce
an effectively infinite height. This negated any variability in the z-direction and reduced
the solution to an effective 2-D case. Additionally, the dispersion rate in the z-direction
43
was set to a value sufficiently low (Table 2-1) compared with that specified for the xand y-directions to further negate any solute mass movement in the z-direction that
might have occurred despite the large b-value. The value for vertical dispersion could
not be set to zero exactly because it appears in the denominator of the analytical
solution (see Equation 2-3 below). The analytical solution (Equation 2-2) solved using
3DADE is given in Leij and Bradford (1994) as follows:
C
C= o
4
v
λ t
∫ Λ1(τ )Γ(τ )dτ + 2R ∫0 Λ 2 (τ )dτ
P (t ) R
t
(2-2)
for:
C
C( x, y , z, t ) x = 0 =  0
0
y < 0, z < 0, 0 < t ≤ t 0
otherwise
where:





y −a
y +a
 ×
 − erfc 
Γ(τ ) = erfc 
 ( 4D τ / R )1 / 2 
 ( 4D τ / R )1 / 2 

y
y









z−b
z+b


−
erfc
erfc 
1/ 2 
 ( 4D τ / R )1 / 2 
z
 ( 4Dzτ / R ) 



 µτ   R
Λ1(τ ) = exp −
 
 R   πDxτ
(2-3)
1/2
 (Rx − v τ )2 


 exp −
4RDxτ 


(2-4)
 Rx + v τ 
 vx 
v

erfc 
−
exp
1 / 2 
D
2Dx
(
4
)
τ
RD
x
 x


 v τ − Rx  

v
 µτ  
 + 1 +
Λ 2 (τ ) = exp −
( x + v τ / R )  ×
 erfc 
1/ 2 
Dx
 R  

 ( 4RDxτ )  
 vx
exp
 Dx
 Rx + v τ   4v τ

 − 
erfc 
1/ 2 
(
4
)
τ
RD

x

  πRDx
2
44
1/2



 (Rx − v τ ) 

exp −
4
τ
RD
x


2
(2-5)
and where R is the retardation factor; τ is time; v is porewater velocity; x is the position
in the direction of flow; Dx, Dy, and D z are dispersion coefficients in the x-, y-, and zdirections, µ is the first-order decay rate coefficient; and λ is the zero-order production
rate coefficient.
Setup for testing of SWIFT2D
An important assumption implicit in the analytical solutions presented is that of
uniform uni-directional velocity. However, given the complexity of SWIFT2D’s
mechanistic approach to hydrology, establishing a precisely uniform velocity field was
not possible. To overcome this, and considering that the reactive transport was being
tested and not the underlying hydrology, velocity was controlled by overwriting
hydrodynamic values calculated by SWIFT2D at each time-step. In this way a uniform
velocity was established, and observed discrepancies between numerical and analytical
solutions were therefore known to be attributable to the numerical implementation of the
reactive-transport equation, and not to variability in velocity.
A square test domain was established for SWIFT2D consisting of 101 x 101 cells,
with each cell 100-m in length (Figure 2-3). Such a large domain was necessary given
the decision to test the model for conditions approximating those under which it would
be applied, namely low velocity and high dispersion (Swain et al., 2004), and the
disparity in boundary conditions at the upper and lower borders of the domain. The
analytical solution assumes open boundaries, but modeled domain was applied with noflow boundaries. A constant velocity of 0.05 m/s was applied with a molecular diffusion
of 20 m2/s. For these conditions, the central fifty cells, justified to the left and centered
around the source (Figure 2-3), were the focus region of the domain, and ensured
45
sufficient area remained in the domain to prevent any effect on concentrations within the
focus region due to the discrepancy in boundary conditions.
Molecular diffusion in SWIFT2D is input as a single value that is applied
isotropically in both dimensions of flow. The longitudinal dispersion coefficient (Dl) is
computed in each cell (Equation 2-6) and in each principal direction of flow according to
a function established by Elder (1959) relating flow conditions, depth, velocity, and the
Chezy resistance coefficient according to:
Dl =
Cd Hu (2g )
,
C
(2-6)
where Cd is a coefficient relating longitudinal dispersion to the local velocity; ū is
the local velocity; H is the temporal flow depth; g is acceleration due to gravity; and C is
the Chezy resistance coefficient, related to the Manning’s n according to (Leendertse,
1987):
C=
H1/ 6
.
n
(2-7)
A representative value of 14.3 has been determined for Cd (Harleman, 1966). The total
effective dispersion implemented in the advection-dispersion-reaction equation is then
the sum of the longitudinal dispersion, which may be different for each direction, and
diffusion, which is constant.
The 2-D analytical solution is valid for uni-directional flow. The absence of
transverse velocity therefore prevented any dispersion from occurring in the transverse
direction. In order to simulate 2-D solute transport it was therefore necessary to rely on
the diffusion coefficient to generate dispersion in the transverse dimension. A reaction
rate of -0.000001 s-1 was used to generate constituent decay for the reactive transport.
46
Setup for testing of FTaRSELOADDS
A first-order decay equation was input to aRSE through the XML input file. One
state-variable was specified to represent the transported solute. One parameter, the
reaction rate kr, was input to reproduce the decay reaction. All other conditions were
kept the same as those used for testing SWIFT2D
Results and Discussion
Conservative and reactive transport were simulated using SWIFT2D (Figures 2-4
and 2-5, respectively), and reactive transport using FTaRSELOADDS (Figure 2-4).
Results using SWIFT2D confirm that the model correctly simulates solute transport, and
that these results are reproducible using FTaRSELOADDS.
Benchmarking SWIFT2D
Results for 2-D transport of a non-reactive solute obtained using SWIFT2D (Figure
2-4) compared well with the analytical solution, but showed some disparity at the
concentration front due to the effects of numerical dispersion (Fischer et al., 1979). To
confirm that this was the source of the discrepancy in results the numerical dispersion
(Dn) was calculated as per Swain et al. (2004):
Dn =
(
)
0.5 σ 2i +1 − σ 2i
’
∆t
(2-8)
where σ2 is the variance of the constituent concentration distribution and i is the
computational cell number. When numerical dispersion was added to the value for
dispersion allocated to the analytical solution the discrepancy at the concentration front
is absent, confirming that numerical dispersion is the source of the differences. Close to
the source boundary the differences are greater and cannot be mitigated by
compensating for numerical dispersion.
47
Verifying FTaRSELOADDS
Results of reactive transport obtained using FTaRSELOADDS were essentially
identical to those obtained using SWIFT2D by visual comparison (Figure 2-5). The ADI
solution method implemented by SWIFT2D splits the transport step into two half-steps
for each time-step, with one half-step used to calculate velocity in the x-direction, and
the other the y-direction. This naturally lends itself to comparing the accuracy of
alternate ways of integrating the reactions step of aRSE into the transport step of
SWIFT2D. Three methods were identified and implemented: 1) applying the reactions
after each half-step using the half-step time-step (TRTR, where T=transport and
R=reactions); 2) applying the reaction step once in between the two transport steps,
using the full time-step, (TRT); and 3) applying the reaction step once after both
transport steps using the full time-step (TTR).
Given the closeness of results, visual analysis was unsuitable for comparison. To
quantitatively assess how well the simulated results compared against the analytical
solution throughout the entire model domain, a program was written making use of the
CORSTAT (see Appendix B, Section B4) code (Aitken, 1973) to calculate the Root
Mean Square Error (RMSE) and Nash-Sutcliffe (E) efficiencies (Nash and Sutcliffe,
1970) for each of the concentration points in the SWIFT2D domain, compared with
analytical value at equivalent spatial points in the 2-D analytical domain, according to
Equation 2-9:
T
∑ (O
t
E = 1−
− St
)
−O
)
t =1
T
∑ (O
t
t =1
2
,
(2-9)
2
48
where O is the observed, O the mean observed, and S the simulated value.
Figures 2-6 and 2-7 depict the spatially-interpolated RMSE and Nash-Sutcliffe
results at each grid-point in the domain after 150 and 300 minutes respectively, for the
TRT case. Visual comparison of these results and those obtained using the SWIFT2D
reactions, or either the TTR or TRTR methods, showed no visible differences. To
quantify differences in overall numerical performance between the methods, the
average Nash-Sutcliffe efficiencies for all the domain points were calculated for each
case using the Nash-Sutcliffe values determined for each point after 300 minutes (Table
2-2). In this way it was possible to quantify the performance of each of the linkage
options, from which it appears that the TRTR implementation is the best when taking all
three statistical measures into account.
The two-dimensional presentation of time-variant error statistics in this way also
offers insights into the location of relatively greater and lesser error, as well as its
propagation throughout the domain in time. For instance, in all figures it is clear that the
region closest to the source is subject to the greatest errors. The Nash-Sutcliffe results
in Figure 2-6 also show the expected result of greater discrepancy at the concentration
front (red ring) and the best match in the centre of the domain where source boundary
effects and numerical dispersion effects at the front are least felt. Black regions of the
Nash-Sutcliffe figures indicate that no values were calculated because no solute had yet
reached those points in the domain, thereby generating a null denominator in the NashSutcliffe calculations.
The Nash-Sutcliffe results in both figures also offer validation of the assumption in
the model setup that an enlarged model domain of 101x101 cells would be sufficient to
49
prevent any effects from the no-flow boundaries above and below interfering with the
focus region of the fifty cells centered on the source (Figures 2-4 and 2-5). At these
boundaries, the assumption of an infinitely open horizontal plane implicit to the
analytical solution is no longer met, and we see this disparity reflected in degraded
Nash-Sutcliffe efficiencies in the region of the boundary. However, throughout the bulk
of the domain, and certainly within the central 50 cells (25 cells above and below the
source region), we find excellent matching between numerical and analytical results.
Close comparison of Figure 2-5 and 2-6 corroborates the directionality of the error
propagation that is so visually striking in Figure 2-6. The isolines of Figure 2-5 match
best at approximately +/- 45 degrees to the horizontal, taken from the solute source
point. Greater than this angle and we see the numerical (black and orange) solutions
under-predict compared with the analytical isoline (green). Less than 45 degrees (i.e.
towards the extreme right of the concentration front) we see the models over-predict
relative to the analytical solution. This pattern is clearly reflected in the Nash-Sutcliffe
figure, where we see clear darker blue (higher Nash-Sutcliffe efficiency) arms projecting
out into a lighter blue surrounding area.
Conclusions
A free-form, non-spatial water-quality model was integrated with a spatiallydistributed hydrodynamic model. The resultant tool, FTaRSELOADDS, is a novel
water-quality tool that is spatially-distributed, driven by mechanistic hydrodynamics, and
user-definable. Linkage of the models was validated by demonstrating the ability of the
linked tool to replicate results obtained using the reactive transport functionality of
SWIFT2D when using aRSE to perform the reactions and SWIFT2D the transport.
50
Table 2-1. Quantities and values used in the comparison of SWIFT2D and FTaRSELOADDS against the analytical
solution for 2-D conservative and reactive transport. Variable names as required by SWIFT2D, aRSE or
STANMOD are included where appropriate
Case
Velocity
[m/s]
Retardation
Factor
Analytical
solution
v = 0.05
SWIFT2D
transport and
reactions
U,UP = 0.05
N/A
V,VP = 0.0
RetFac = 1
SWIFT2D
U,UP = 0.05
N/A
transport with
V,VP = 0.0
aRSE reactions
Pulse length
Decay rate
-1
[s ]
T0 = 60000 s µ = 1E-5
Transverse
Longitudinal (x)
horizontal (y)
dispersion
dispersion
2
[m /s]
2
[m /s]
Dx = 20.5332
Dy = 20
Transverse
vertical (z)
dispersion
[m2/s]
Unit concentration
source dimension [m]
Dz = 1E-10
-a to a (y-direction):
|a| = 100 m;
-b to b (z-direction):
|b| = 1E+10 m
TRBNDA = 1
DIFDEF = 20
for TITI = 0 to AKK = 1E-5
Dl = 0.5332*
1000 min
DIFDEF = 20 N/A
2 x 100 m cells (N,M):
Cell (50,1) and (51,1)
TRBNDA = 1
for TITI = 0 to Kr = 1E-5
1000 min
DIFDEF = 20 N/A
2 x 100 m cells (N,M):
Cell (50,1) and (51,1)
DIFDEF = 20
Dl = 0.5332*
*Dl calculated from Equations 2-6 and 2-7 for n = 0.03 s/m1/3, H = 0.50 m, ū = 0.05 m/s, g = 9.801 m/s2, Cd = 14.3
51
Table 2-2. Nash-Sutcliffe efficiencies obtained for different methods of integrating
aRSE reactions into FTLOADS
SWIFT2D
aRSE: TTR
aRSE: TRTR aRSE: TRT
Average
0.92843577
0.94792578
0.94790868
0.94789519
Mode
0.99854711
0.98674260
0.99906814
0.99443873
Median
0.99463456
0.99467713
0.99466211
0.99464882
Figure 2-1. Schematic detailing the architecture of the code linking the surface-water
model in FTLOADDS (SWIFT2D) with a Reaction Simulation Engine (aRSE).
52
Figure 2-2. Source boundary condition for analytical solution: Third-Type, flow in the xdirection, source dimension a = 100 m in horizontal transverse y-direction,
source dimension b = 1E+10 (~infinity) in the vertical transverse z-direction
(from Leij and Bradford, 1994).
53
Figure 2-3. SWIFT2D model domain used for comparison of conservative and reactive
transport simulations with analytical solutions; red indicate source cells, all
cells 100 m square, total domain 10,000 m, no-flow boundaries at N=1 and
N=101, and M=1.
54
Figure 2-4. Concentration isolines for 2-D conservative transport from a small
rectangular source as determined by SWIFT2D (black), the analytical solution
(green), and the analytical solution with numerical dispersion effects
accounted for (orange).
55
Figure 2-5. Concentration isolines for 2-D reactive transport from a small rectangular
source as determined by SWIFT2D (black), the analytical solution (green),
and the coupled version of FTLOADDS and aRSE (orange).
56
Figure 2-6. Spatially-interpolated RMSE (left) and Nash-Sutcliffe efficiencies (right)
after 150 minutes of simulation for the case of transport-reactions-transportreactions.
Figure 2-7. Spatially-interpolated RMSE (left) and Nash-Sutcliffe efficiencies (right)
after 300 minutes of simulation for the case of transport-reactions-transportreactions.
57
CHAPTER 3
MODELING HYDROLOGY IN THE SOUTHERN INLAND AND COASTAL SYSTEMS
Introduction
There are two major paths of natural freshwater flow from the Everglades into
Florida Bay. One pathway, Taylor Slough, empties directly into the Bay, while the other
pathway, Shark River Slough, contributes a portion of its flow to Florida Bay, but
discharges primarily into the Gulf of Mexico. Freshwater inputs are vital to the coastal
Everglades ecosystem, having important impacts reaching as far as the Florida Keys
(SFWMD and FDEP, 2004). In particular, changes to the flow patterns are expected to
have consequences for water-quality in Taylor Slough, adjacent wet prairies, and the
coastal estuaries into which they empty (Childers, 2006). Modeling the region’s
hydrology is the first phase of an effort to model the phosphorus water-quality using a
new water-quality model for the region.
Previous Hydrological Modeling of SICS
Numerous modeling and experimental studies have been undertaken to better
understand the hydrodynamics within the SICS region. For many years, the South
Florida Water Management Model (SFWMM; MacVicar et al., 1984) was used to
provide regional hydrologic information at a 2-mile by 2-mile spatial scale. The coarse
spatial resolution made SFWMM unsuitable for the detailed analysis required to
determine local water management needs and support mechanistic water-quality
modeling efforts.
The South Florida Regional Simulation Model (SFRSM; Brion et al., 2000) was,
and continues to be, developed to replace the SFWMM. Though SFRSM employs a
variable-resolution triangular mesh for spatial discretization, like its predecessor it too
58
neglects inertial forces, and flow volumes are consequently less accurate. Also
neglected are variable-density and unsteady flow conditions, which are important
characteristics of the SICS region because of tidal interactions with Florida Bay and
wind-shear effects (Swain et al., 2004). Results from efforts to simulate coastal flows to
Florida Bay using SFWMM (Hittle, 2000) were undermined by greatly amplified
freshwater flows, which in turn diluted coastal salinities. Lin et al. (2000) attempted to
use FEMWATER123 for the region, but the computational demands of the model, which
simulates 1-D canal flow, 2-D overland flow, and 3-D finite-element ground-water flow,
were restrictive.
The failure of these models to meet the persistent need for greater accuracy and
spatial resolution of the simulated hydrologic conditions in SICS (as a necessary input
for ecological modeling efforts using ATLSS) and freshwater inputs to Florida Bay
(needed for hydrodynamic modeling of Florida Bay) led to an extensive modeling effort
by the USGS that included a number of field studies to quantify physical parameters.
The major product of this effort was the development of the SICS model, an application
of the USGS-developed Surface-Water Integrated Flow and Transport in 2-Dimensions
(SWIFT2D) hydrodynamic/transport model with additional enhancements specifically for
the coastal wetlands of the Everglades (Swain et al., 2004; Swain 2005).
Variable-density ground-water simulation was integrated into the SICS application
by Langevin et al. (2005). The effort entailed linking SWIFT2D with SEAWAT, a version
of the 3-D modular ground-water flow model MODFLOW integrated with the 3-D
modular transport model MT3DMS, which can simulate variable-density ground-water
hydrology. The resultant tool is known as Flow and Transport in a Linked Overland-
59
Aquifer Density Dependent System (FTLOADDS), which was subsequently adapted
further for the Tides and Inflows in the Mangroves of the Everglades (TIME) application
(Wang et al., 2007). The TIME application not only encompasses the SICS region, but
greatly expands the domain to include all of Everglades National Park and Big Cypress
National Preserve. Versions 1.0 and 1.1 of FTLOADDS refer to the original SICS
applications using only SWIFT2D. Version 2.1 refers to the coupled surfacewater/ground-water SICS application, and version 2.2 the coupled surfacewater/ground-water TIME application (see Appendix A for further details on versions).
Remodeling the Hydrology of SICS
The proposed effort to model water-quality in the SICS region using
FTaRSELOADDS requires a suitable hydrologic application to provide the necessary
hydrodynamic drivers of water-quality. The original SICS application, which did not
include ground-water simulation, was selected for the inaugural application of
FTaRSELOADDS based on a number of considerations: 1) the surface-water results
obtained with this simplified version of FTLOADDS were considered sufficient for such
testing; 2) the water-quality focus was on surface-water conditions, so only SWIFT2D
had been coupled with aRSE (see Chapter 2); 3) the concerns about compounding
computational times given the addition of aRSE to an already computationally intensive
tool.
However, a number of changes have been made to the SWIFT2D code in
FTLOADDS as the tool has evolved to the current form (version 2.2), which were not
present when the original SICS application (version 1.1) selected for testing
FTaRSELOADDS was established. It was therefore necessary to evaluate the effects of
these changes, many of which were simplifications, on the simulation of surface-water
60
hydrology in SICS. In particular, the effect of removing depth-varying Manning’s n
needed to be evaluated to assess the implications for water-quality modeling.
Materials and Methods
Model Description
The 2-D, vertically integrated, unsteady flow and transport model SWIFT2D has its
origins in SIMSYS2D (Leendertse, 1987), which in turn built on earlier work conducted
throughout the 1970’s by Leendertse and his colleagues at The Rand Corporation to
develop a water-quality simulation model for well mixed estuaries and coastal seas
(Leendertse, 1970; Leendertse and Gritton, 1971; Leendertse, 1972).
SWIFT2D governing equations
Thorough descriptions of the SWIFT2D governing equations and their numerical
implementation are variously provided in Leendertse (1987), Goodwin (1987), Bales
and Robbins (1995), and Schaffranek (2004). Four partial-differential equations are
used to describe unsteady, non-uniform, variable-density, turbulent fluid motion
(Equations 3-1 to 3-3) and solute transport (Equation 3-4), which are formulated
according to the laws of Conservation of Mass and Conservation of Momentum.
Hydrodynamics are described with the two-dimensional Saint-Venant equations (de
Saint-Venant, 1871; Equations 3-2 and 3-3), which are derived from the Navier-Stokes
equations by applying temporal averaging of velocity, pressure and mass over timeintervals that are long relative to the time-scale of turbulent fluctuations, and assuming
negligible vertical accelerations. Transport is described by the advection-dispersionreaction equation (Equation 3-4). The resultant formulations retain nonlinear advective
and bottom-stress terms, which permit the simulation of eddies and residual circulation,
and coupled motion and transport with time-varying horizontal density gradients:
61
∂ζ
∂(HU ) ∂(HV )
+
+
= 0,
∂t
∂x
∂y
(3-1)
∂U
∂U
∂V
∂ζ gH∂ρ
U 2 + V 2 θρaW 2 sin ψ
+U
+V
− fV + g
+
+ gU
−
∂t
∂x
∂y
∂x 2ρ∂x
C 2H
ρH
2
2
∂ U ∂ V 
− k  2 + 2  = 0 ,
∂y 
 ∂x
(3-2)
∂V
∂U
∂V
∂ζ gH∂ρ
U 2 + V 2 θρaW 2 cos ψ
+U
+V
− fU + g
+
+ gV
−
∂t
∂x
∂y
∂y 2ρ∂y
C 2H
ρH
2
2
∂ V ∂ U 
− k  2 + 2  = 0 , and
∂y 
 ∂x
∂(HP ) ∂(HUP ) ∂(HVP ) ∂(HDx ∂P / ∂x ) ∂(HDy ∂P / ∂y )
+
+
−
−
+ HS = 0 ,
∂t
∂x
∂y
∂x
∂y
where:
C = Chezy resistance coefficient coefficient;
Dx ,Dy = diffusion coefficients of dissolved substances;
f
g
h
H
= Coriolis parameter;
= acceleration due to gravity;
= distance from horizontal reference plane to channel bottom;
= temporal flow depth (h + ζ );
= horizontal exchange coefficient;
= vector of vertically averaged dissolved constituent concentrations;
= source of fluid with dissolved substances;
= vertically averaged velocity component in x direction;
= vertically averaged velocity component in y direction;
= wind speed;
ζ = water - surface elevation relative to horizontal reference plane;
θ = wind stress coefficient;
ρ = density of water;
ρa = density of air; and
k
P
S
U
V
W
ψ = angle between wind direction and the positive y direction.
62
(3-3)
(3-4)
SWIFT2D numerical solution technique
The governing differential equations cannot be solved analytically unless
subjected to simplifying assumptions that are unacceptable for the intended
applications. A finite difference numerical solution technique is therefore applied to a
computational domain of equally spaced grid points. The finite-difference equations are
solved on a space-staggered grid (Figure 3-2) using the alternate-direction implicit (ADI)
method. Velocity points are located between water-level points to produce an efficient
solution of the continuity equation (Leendertse, 1987). The ADI method splits the timestep to obtain a multidimensional implicit solution that provides second-order accuracy,
and requires only the inversion of a tridiagonal matrix in order to solve each set of finitedifference equations (Roache, 1982). Detailed descriptions of the finite difference
equations are provided in Swain (2005).
Though the ADI method is unconditionally stable (Leendertse, 1987) there are
practical limitations to the time-step (Roache, 1982), particularly when applied to
irregularly shaped domains (Weare, 1979) or complex bathymetries (Benque et al.,
1982).
SWIFT2D code enhancements and simplifications
The FTLOADDS code presently available is that of version 2.2. The original SICS
application represents FTLOADDS version 1.1, which included enhancements to
SWIFT2D but no ground-water linkage (see Chapter 2). These enhancements were
maintained with only minor changes to the SWIFT2D code due to the coupling process
in FTLOADDS version 2.1. However, SWIFT2D code was significantly modified in the
course of the model’s evolution to version 2.2. This has implications for this effort to
reproduce SICS surface-water results originally obtained using SWIFT2D v1.1.
63
SWIFT2D in FTLOADDS v1.1. The original effort to model surface-water flow in
the SICS region required a number of modifications to the SWIFT2D model (Swain et
al., 2004):
•
Precipitation: The rainfall code was adapted to permit spatially-distributed values for
rainfall volume to be added to individual cells. Rainfall inputs were calculated at 15minute intervals by kriging the rainfall from 14 different rainfall stations in the region.
Rainfall was not added to dry cells, which implicitly assumed that when rainfall fell on
dry cells it infiltrated into the ground-water.
•
Evapotranspiration: Evapotranspiration (ET) was not included in the original
SWIFT2D v1.0 code, which was intended for application to estuaries and coastal
waters where evaporation could be considered negligible and macrophytes
sufficiently sparse to ignore transpiration. For SWIFT2D v1.1 an equation regressing
ET with solar radiation and depth (German, 2000) was applied to each cell to
determine spatially-distributed, time varying ET.
•
Depth-varying Manning’s n: When up-scaling point measurements of frictional
resistance to grid-scale representative values, microtopography can increase the
effective frictional resistance at lower depths. To address this, an empirical relation
was applied to determine an effective Manning’s n (neff) based on a reference input
value (n, measured or estimated), a reference depth (dref, the assumed depth at
which measurement or estimation was conducted), the actual depth (d), and a power
variable (p) to capture non-linear effects (Swain et al., 2004):
neff
 d
= n
 d ref
p

 ,

(3-5)
•
Wind-sheltering: To account for the sheltering effects of vegetation (Jenter, 1999),
which were not considered for open-water applications of SWIFT2D v1.0, a spatially
uniform sheltering coefficient was applied to all vegetated cells (considered those
having a Manning’s n greater than 0.1).
•
Other: Other changes included technical modifications to the treatment of flow
adjacent to barriers (which were not previously permitted to go dry), wind friction in
cells adjacent to water-level boundaries (set to zero to avoid numerical oscillations),
and output printing routines.
SWIFT2D in FTLOADDS v2.2. The coupling of SWIFT2D to SEAWAT through
leakage required additional code, but left each of the models intact such that SWIFT2D
could be run without the need to call SEAWAT if so desired. However, the progression
64
from SICS application to TIME application introduced new changes to SWIFT2D (Wang
et al., 2007):
•
Precipitation: Rainfall in version 2.1 was specified at 15-minute intervals and
spatially-interpolated from 14 stations for each cell. Rainfall in version 2.2 is
spatially uniform over defined zones, of which SICS represents one (i.e. uniform
rainfall over the entire domain), and is specified as 6-hour averages. Additionally, the
wetting and drying algorithm has been modified such that rewetting is now permitted
to occur directly from rainfall recharge.
•
Evapotranspiration: In analogous fashion to rainfall, ET is now applied regionally,
and therefore uniformly over the SICS domain, also as 6-hour averages.
Additionally, the modified Penman method (Eagelson, 1970) has replaced the cellby-cell ET calculations (Swain et al., 2004). When depth of ET is greater than 10
percent of the remaining depth of water then ET is instead removed from the first
layer of the ground-water to avoid making the cell go dry or the depth go negative.
When the ground-water module is turned off this effectively means no ET occurs.
•
Manning’s n: The functionality to treat variation of Manning’s n with depth of flow
was removed from SWIFT2D due to concerns over its empirical nature (E.D. Swain,
U.S. Geological Survey, personal commun., 2010). Frictional resistance (Chezy)
terms, which are calculated using depth and Manning’s n, are now defined at cell
faces rather than at cell centers. This permits a different resistance in each of the
principal directions of flow, but also requires a second Manning’s n-value for each
cell. In version 2.1 obstruction to surface-water flow, most notably the Buttonwood
Embankment, was defined using the original SWIFT2D barrier formulation intended
to represent weirs. Coastal rivers and creeks were defined as low barriers with
calibrated flow coefficients. In version 2.2 the coastal embankment is defined by a
modified cell-face frictional resistance term, with creeks represented as gaps with
specified (reduced) friction terms.
Considering the important roles played by both precipitation and ET in the south
Florida water budget (Sutula et al., 2001), and of Manning’s n in determining flow
velocities and wet/dry conditions, the modifications to v2.2 described above represent
significant hydrological simplifications to the SWIFT2D model. This effort to model
SICS hydrology therefore represented an effort to study the effects of these model
simplifications on the ability of SWIFT2D to simulate hydrodynamics in the SICS region
for future water-quality application.
65
Model Setup
The SWIFT2D v1.1 model setup used in the original SICS application was
reapplied as consistently as possible in an effort to reproduce the original results for the
period of August 1996 through August 1997. All effort was made to maintain the same
model setup and parameterization, and the integrity of the original SICS application
should be assumed intact unless changes are specified below. Figures from the USGS’
SICS modeling report (cited as Swain et al., 2004) are reproduced where model setup is
appropriately consistent, and original figures have been produced where necessary.
Computational domain
The previously established SICS model (Swain et al., 2004) domain (Figure 3-3),
comprising 9,738 square computational cells of length 304.8 m (1000 ft) for a total
domain area of 905.8 km2, was applied with minimal changes to the model boundary.
The new treatment of frictional resistance terms at cell faces, rather than cell centers,
generated a number of points on the domain boundary where floating point problem
arose due to the underlying space-staggered grid geometry. The original version
required resistance terms for each cell in the computational domain, which is defined
row-by-row, and column-by-column, to produce the irregular boundary required.
Resistance terms were calculated based on input Manning’s n values, which were
specified as zero outside the active domain. Since the original computational domain
was not defined to intentionally account for the additional cell face values required by
the current version, and given that the space-staggered grid used by SWIFT2D
attributes values originating in, for example, cell (m, n+1) to cell (m, n), instances of
Chezy resistance terms being calculated using Manning’s n values of zero in the
66
denominator arose. This was resolved by eliminating the offending individual boundary
cells from the computational row or column as the case arose.
Land-surface elevations were measured at about 400-m intervals (Desmond et al.,
2000) and a linear distance-weighted four-point interpolation was applied to assign land
surface elevations to each computational cell (Figure 3-4). The Buttonwood
Embankment (Figure 3-1) is a significant hydrologic barrier in the region, which
separates the freshwater wetlands from Florida Bay. Most exchange of water occurs
through the many creeks that traverse the embankment. Physically, the embankment is
an elevated region, but in SICS it is simulated by barriers based on large resistance
terms in the direction of flow, interspersed with lower resistance values where creeks
cut through the barrier.
Boundary conditions
Boundary conditions (Figure 3-5) were provided at the water surface and lateral
boundaries. The water surface boundary is assumed to be horizontal in each cell; water
is permitted to move vertically but no deformation of the water surface within the cell is
considered. Physically, this implies that high-frequency surface waves are not
accounted for in the model.
A uniform rainfall rate was supplied as a model input file containing values
calculated as the arithmetic mean of all stations in the SICS region, averaged over 6hour intervals. A uniform ET rate was similarly supplied as an input file, rather than
calculated within the model. Input ET values were calculated as the regional mean of
ET values calculated according to the modified Penman method (Wang et al., 2007).
Wind conditions are represented as spatially uniform across the entire domain, and the
data from the Old Ingram Highway site was used to define the wind field. A moving
67
average wind speed was used for the boundary condition since fluctuations in wind
conditions at sub-hourly time-scales are considered to not generally be representative
of regional patterns, which is the scale implied when uniformly applying wind.
Lateral boundaries are described as open (free exchange with water and solutes
across the boundary) or closed (no flow or exchange). Open boundaries were
described by time-series inputs for either discharge or water-level. The SICS model
lateral boundaries are identified in Figure 3-5, and include seven constant head
boundaries and three discharge source boundaries. The discharge sources (Figure 36) are at Taylor Slough Bridge, the C-111 pumping station, and within the L-31W canal.
Inflow at Taylor Slough Bridge was determined from stage-discharge data at the Taylor
Slough Bridge site, and at the L-31W site according to stage-discharge relationship at
the S-175 hydraulic gate structure, where this flow originates. Input of discharge at C111 source is based on the discharge from pumping station S-18C, occasionally
adjusted to compensate for flows directly out of the canal and into Florida Bay when the
S-197 structure is opened. The levee on the southern side of the C-111 section has
been removed to promote delivery of additional water to the SICS region. An artificial
topographic low along the SICS boundary was applied to facilitate more uniform flow
distribution along the lower section of C-111.
Several regional model parameters are required and applied as per Swain et al.
(2004): air density, latitude (single value), kinematic viscosity of water, wind stress
coefficient, unadjusted horizontal mixing coefficients, isotropic mass dispersion
coefficient, a coefficient relating mass dispersion to flow conditions, a resistance
68
coefficient for each computational cell and for tidal creeks, and marginal depth (Swain et
al., 2004).
Stability considerations
Although the ADI method is unconditionally stable (Leendertse, 1987), the
treatment of flow barriers introduces practical limitations. Experimentation with the timestep eventually lead to selection of a half-step of 1.5 minutes, which demonstrated
sufficiently stability in the region of the creeks and barriers. The next-largest possible
half-step was 2.5 minutes, based on the fact that full time-steps needed to be
compatible with the time-steps defined for tidal boundary conditions, which are read in
at 15-minute intervals, and this proved to be unstable.
Given the simulation of salinity transport it was also necessary to consider
numerical dispersion. A diffusion coefficient of 10 m2/s was applied based on the
previous application of SICS v1.1. (Swain et al., 2004). Considering the cell dimensions
of 304.8 m, and a conservative (high) estimate for average velocities on the order of
0.05 m/s (based on previous results in Swain et al., 2004), a Péclet number of
approximately 1.5 was obtained, which even though conservative was below the
generally applied upper limit of 2.
Results and Discussion
Water-level results at the 12 observation stations in the SICS domain are
presented first, followed by an assessment of the flow through the creeks linking Florida
Bay to Taylor Slough. Following thereafter are 2-D results for water-level, flow, and
salinity.
69
Water-Level Results
Simulated stages at each of the 12 water-level stations are presented in Figures 37 and 3-8. Results are divided between those stations that fall within Taylor Slough
(Figure 3-7), which are more directly subject to discharges from the TSB source, and
stations east of the slough (Figure 3-8) that are more directly affected by flows
originating from the C-111 canal. The area of the time-series figures shaded in brown
indicates the subsurface. Where brown meets blue corresponds to ground-surface
elevation for the cell containing the location of the station. The area shaded in blue
indicates the maximum observed water-level during the model validation period from
July of 1996 to August 1997. Observed water-levels are depicted in blue, and can drop
below the ground surface because water-level observations are recorded by wells. The
results obtained using SWIFT2D v1.2 are shown in black. Periods where simulated
results are not depicted correspond to conditions that SWIFT2D considers dry, which
occur when water depth drops below 5 cm. As can be seen in both figures, this
happened regularly for a number of locations, including two critical phosphorus
concentration observation locations, the EPGW and P37 stations.
Significant effort was expended attempting to resolve this. The final solution was to
reintroduce the functionality of depth-varying Manning’s n, which had been removed in
the present version (v1.2). The reintroduction of depth-varying Manning’s constitutes an
updated version of 1.2, and is designated version 1.2.1 (red results in Figures 3-7 to 310). In the original SICS v1.1 modeling effort, the variables applied to the nominal
Manning’s input, dref and p (Equation 3-5), were 0.6 m and 2 respectively. In this version
1.2.1 the reference depth was set to 0.4 m given the absence of almost any depths of
70
0.6 m in the simulated year, making such an assumption for the reference depth
questionable. The simple non-linear quadratic power was maintained.
A comparison of the results obtained in this work with those from the original SICS
modeling effort (Swain et al., 2004) is given in Figures 3-9 and 3-10, with statistics
comparing all three versions – original SICS application (v1.1), present SICS application
with depth-constant Manning’s n (v1.2), and present SICS application with depthvarying Manning’s n (v1.2.1) – are presented in Table 3-1, and summarized in Table 32.
Visual comparison of the results in Figures 3-7 to 3-10 with the statistics in Table
3-1 reveals some contradictions. Visually, it is clear that the results obtained using
depth-varying Manning’s n (in both SICS 1.1 and 1.2.1) are a better representation of
reality insomuch as periods of wetness and dryness are captured more reliably,
particularly for the critical water-quality stations EPGW and P37. In SICS v1.1 (Figures
3-9 and 3-10) we see a tendency on the part of the model to over-predict water-levels,
especially at the beginning of the simulation and the beginning of the second wetseason. The current application performs much better in this regard. Conversely, in
SICS v1.2 (Figures 3-8 and 3-9), the lack of depth-dependency in flow resistance
results in excessively rapid drying out of the system when data clearly shows that wet
conditions prevail. Version 1.2.1 avoids the drawback of both of these versions, better
predicting the dry-down following wet periods compared with SICS v1.2 and avoiding
the over-predictions that were characteristic of SICS v1.1.
The Nash-Sutcliffe efficiencies presented in Table 3-1 and summarized in Table 32 do not capture this, instead implying that v1.2 offers the best results. This is a
71
consequence of the fact that periods of dry conditions are not accounted for in the
Nash-Sutcliffe calculations because there is no simulated depth value against which to
compare the observed value. The result is a failure to capture the full extent of the
error, and exposes a weakness of this error statistic for assessing results in shallow
systems where wetting and drying is frequent. Additionally, the EP12R station has very
low Nash-Sutcliffe results which disproportionately reduce the Nash-Sutcliffe statistics
(Tables 3-1 and 3-2) considering how little data is actually present for this station
(Figure 3-9). Furthermore, the station is located very close to the boundary of the
model, a region that is known to be susceptible to greater errors due to boundary effects
(Leendertse, 1987).
Figure 3-11 to 3-13 shows the frequency and cumulative distribution of NashSutcliffe results for all stations, Taylor Slough stations, and C-111 wetlands stations
respectively, from SICS v1.2.1. Over 40 percent of all the stations attained NashSutcliffe efficiencies of 0.7 or higher, and approximately 60 percent of 0.5 or higher.
Performance of the model for simulating water-levels in Taylor Slough (Figure 3-12) was
comparable to that for the C-111 wetlands (Figure 3-13).
It is known that bias can lead to misleading Nash-Sutcliffe efficiencies (McCuen et
al, 2006). Furthermore, indication of a tendency to over-predict or under-predict would
be useful in interpreting how the changes made to SICS have affected the models
ability to capture particular conditions, which would be useful in future water-quality
modeling efforts.
Simulated results from SICS v1.1. and v1.2.1 were plotted against analogous
observational data. For the 6 stations in the vicinity of Taylor Slough (Figure 3-12) we
72
see a general reduction in variability about the 1:1 line for SICS v1.2.1 compared with
v1.1. Stations higher up the slough (R127 and TSH) are the exception, tending towards
over-prediction at shallow depths and under-prediction otherwise. For the C-111
stations (Figure 3-13), the current SICS v1.2.1 offers marked improvements, indicating
that v1.2.1 is better equipped to handle the conditions of both slough (Taylor Slough
area of SICS) and marl prairie (C-111 wetlands area). In particular, results were greatly
improved for the EVER4 station and, importantly for water-quality, the EPGW station.
The poor results obtained for EP12R appear to be a problem in both versions of the
model. Since both versions apply some form of depth-varying Manning’s coefficient,
while version 1.2, which has better results for EP12R according to the Nash-Sutclife
efficiencies previously discussed, does not account for changing resistence with depth,
this may be a consideration. If the EP12R site is sparsely vegetated then the depthvarying effect will be less important, and may then be a reason for this discrepancy.
Water-levels throughout the SICS region are presented on the first of each month,
from August 1996 to July 1997, in Figures 3-14 (first wet season), Figure 3-15 (dry
season), and Figure 3-16 (end of dry season and start of wet season). Two-dimensional
results are presented beneath time-series figures depicting precipitation and discharge
source inputs to the domain during that period to facilitate visual comparison between
inputs and hydrologic conditions.
Discharge Results
Discharge data were available for five creeks in the Buttonwood Embankment.
Figure 3-17 compares the simulated daily averaged flow rates in SICS v1.2.1 with the
observed daily averaged flow rates. These results are important for assessing the
accuracy of fluxes, which are critical if loading rates are to be estimated. They are also
73
an important consolidation of depth and velocity simulations; given the reliable depth
results described above, reliable flux results therefore indicate reliable velocities, which
are important for the transport of solutes in water-quality modeling.
In all creeks except McCormick Creek, the magnitude and timing of daily average
fluxes were satisfactory. Vector diagrams depicting flow direction and magnitude are
given for the first of each month in Figures 3-18 to 3-20. Results reproduce well the
trends found in Swain et al. (2004) that show tendency for flow from both Taylor Slough
and C-111 to congregate in the region of Joe Bay. It is therefore important that the two
primary creeks in this region, Taylor Creek and Mud Creek, are well modeled since they
represent a significant portion of the Taylor Sough flow output to Florida Bay. The large
fluxes through Trout Creek and the directionality of fluxes towards it from the C-111
canal indicate its importance for inputs to Florida Bay originating from the eastern region
of SICS. Fluxes are probably particularly large through Trout Creek because of its
position between two large water bodies that hold relatively deep water permanently
compared with the shallow and intermittently wet/dry conditions on the landward side of
Taylor Creek and Mud Creek.
Salinity Results
Figures 3-21 to 3-23 present the two-dimensional spatial results for salinity
distribution throughout SICS on the first of each month. These results illustrate the
significant diluting effect of freshwater inputs from Taylor Slough and C-111 to Florida
Bay during high flow periods. Salinities were substantially higher throughout the Bay in
the dry season. Dilution emanated from the region of Joe Bay following high freshwater
flows, as would be expected given the previously discussed flow results. During peak
dry periods there is marked intrusion of salinities into the coastal wetlands in the eastern
74
regions of SICS. Particularly high salinities may be due to evapotranspiration of water
with increased salinity due to tidal influxes during low-flow periods. Such water may
also become trapped in depressed regions by surrounding dry land after tides have
withdrawn.
Conclusions
The current working version of SWIFT2D (v1.2) does not contain depth-varying
Manning’s resistance. This proved to undermine the ability of the mode to accurately
capture wet and dry conditions, which are important for both practical considerations
(given the paucity of phosphorus data points for testing in Chapter 4) and
biogeochemical considerations (since wet conditions determine the presence or
absence of aquatic processes). When depth-varying Manning’s n was reintroduced into
the model in version 1.2.1 this problem was overcome. Water-levels throughout the
SICS region and discharge rates for important creeks were captured well. The reliable
simulation of wet and dry conditions and velocities therefore established a satisfactory
foundation for mechanistic water-quality modeling of the region.
It is possible that the reintroduction of ground-water exchange may negate the
need for depth-varying Manning’s n. Under very shallow flow conditions, which is when
depth-varying Manning’s would be most important, the small surface-water hydraulic
head may lead to ground-water upwelling into the water column. Other modeling efforts
in the region have shown that ground-water inputs likely occur during the dry season
(Langevin et al., 2005), with possible implications for phosphorus loading to the surface
water as well (Prince et al., 2006). In the absence of ground-water exchange, the
calibration of the depth-varying Manning’s parameters dref and p to maintain surfacewater heads that would otherwise dissipate (as shown in the results for v1.2) equates to
75
compensating for the lack of ground-water upwelling that may actually be occurring.
Consequently, a fully coupled surface-water/ground-water simulation of SICS using
version 1.2 may be sufficient to justify the assumption of depth-invariant Manning’s n.
However, for the purpose of testing the phosphorus water-quality model, water-levels
under shallow conditions are sufficiently sensitive to require that depth-varying
Manning’s be included.
76
Table 3-1. Nash-Sutcliffe efficiencies for water-level observation points in SICS
Station
SICS v1.1*
SICS v1.2**
SICS v1.2.1***
CP
0.7201337
0.901839
0.8771178
P67
0.2144507
0.7837026
0.8087565
TSH
0.7313131
0.8232658
0.7899594
P37
0.7620635
0.863053
2.44E-02
E146
0.778919
0.8662752
0.8897558
EVER5A
-0.1176481
0.6932715
0.3337759
EVER7
0.5472993
0.7139693
0.8710759
EPGW
0.4939922
9.81E-02
0.4452754
EVER6
0.8514937
0.6204761
0.8550127
EP12R
-2.930052
-1.618115
-4.148942
EVER4
0.5493984
0.8272943
0.6898439
R127
0.5810636
0.5898135
0.4134087
* Calculated from digitized results in Swain et al., 2004
** Manning’s n held constant with depth of flow
*** Manning’s n varied with flow depth according to Equation 3-5
Table 3-2. Nash-Sutcliffe statistics for stations in the viciniy of Taylor Slough, stations in
the vicinity of C-111, and all stations in the SICS region.
SICS v1.1*
SICS v1.2**
SICS v1.2.1***
Taylor Slough stations
Mean
0.6313
0.8047
0.6339
Standard Error
0.2159
0.1128
0.3463
Median
0.7257
0.8432
0.7994
Kurtosis
3.7805
3.4693
1.0346
Skewness
-1.9502
-1.7921
-1.4219
C-111 stations
Mean
-0.1009
0.2225
-0.1590
Mean (excl EP12R)
0.4649
0.5906
0.6390
Standard Error
1.4219
0.9371
1.9666
Median
0.5206
0.6569
0.5676
Kurtosis
4.9453
4.4112
5.7462
Skewness
-2.1940
-2.0892
-2.3836
All stations
Mean
0.2652
0.5136
0.2375
Mean (excl EP12R)
0.5557
0.7074
0.6362
Standard Error
1.0423
0.7052
1.4085
Median
0.5652
0.7488
0.7399
Kurtosis
9.9357
9.1905
10.8236
Skewness
-3.0767
-2.9601
-3.2369
* Calculated from digitized results in Swain et al., 2004
** Manning’s n held constant with depth of flow
*** Manning’s n varied with flow depth according to Equation 3-5
77
Figure 3-1. Location of the Southern Inland and Coastal Systems study area (from
Swain et al., 2004).
78
Figure 3-2. Space-staggered grid system showing relative locations of hydrodynamic
characteristics.
79
Figure 3-3. The SICS computational grid, showing the location of Taylor Slough, the
Buttonwood Embankment and the coastal creeks (from Swain et al., 2004).
80
Figure 3-4. Land-surface elevations (from Swain et al., 2004).
81
Figure 3-5. Location of SICS model boundary conditions, including specified water-level
boundaries and discharge sources (from Swain et al., 2004).
82
Figure 3-6. Specified hydrologic inputs to SWIFT2D: discharge on the bottom axis and
rainfall on the top axis. The three principal seasons, wet interspersed by dry,
during the course of the simulation are depicted.
83
Figure 3-7. Water-levels at the six stations in the vicinity of Taylor Slough, simulated with depth-varying Manning’s n
(v1.2.1 - red) and with constant Manning’s n (v1.2 – black).
84
Figure 3-8. Water-levels at the six stations in the vicinity of C-111, simulated with depth-varying Manning’s n (v1.2.1 - red)
and with constant Manning’s n (v1.2 – black).
85
Figure 3-9. Water-levels at the six stations in the vicinity of Taylor Slough, simulated with depth-varying Manning’s n in
the current version (v1.2.1 - red) and the original SICS application (Swain et al., 2004; v1.2 – black).
86
Figure 3-10. Water-levels at the six stations in the vicinity of C-111, simulated with depth-varying Manning’s n in the
current version (v1.2.1 - red) and the original SICS application (Swain et al., 2004; v1.2 – black).
87
Figure 3-11. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies
attained with SICS v1.2.1, for all 12 water-level stations.
88
Figure 3-12. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies
attained with SICS v1.2.1, for 6 water-level stations in the vicinity of
Taylor Slough.
89
Figure 3-13. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies
attained with SICS v1.2.1, for 6 water-level stations in the vicinity of C111.
90
OBSERVED WATER-LEVEL
Figure 3-12. Trends in prediction bias for the 6 stations in the vicinity of Taylor
Slough.
91
OBSERVED WATER-LEVEL
Figure 3-13. Trends in prediction bias for the 6 stations in the vicinity of C-111.
92
Figure 3-14. Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the first four months (first wet season). White space
within the domain indicates dry cells.
93
Figure 3-15. Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the middle four months (dry season). White space
within the domain indicates dry cells.
94
Figure 3-16. Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the final four months (up to the second wet season).
White space within the domain indicates dry cells.
95
Creek discharge (cubic meters per second)
Figure 3-17. Simulated and measured discharges through five gauged creeks in
the Buttonwood Embankment
96
Figure 3-18. Rainfall and discharge inputs, and corresponding 2-D discharge
vector distributions for the first four months (first wet season).
97
Figure 3-19. Rainfall and discharge inputs, and corresponding 2-D discharge
vector distributions for the middle four months (dry season).
98
Figure 3-20. Rainfall and discharge inputs, and corresponding 2-D discharge
vector distributions for the final four months (up to the second wet
season).
99
Figure 3-21. Rainfall and discharge inputs, and corresponding 2-D salinity
distributions for the first four months (first wet season). White space
within the domain indicates dry cells.
100
Figure 3-22. Rainfall and discharge inputs, and corresponding 2-D salinity
distributions for the middle four months (dry season). White space
within the domain indicates dry cells.
101
Figure 3-23. Rainfall and discharge inputs, and corresponding 2-D salinity
distributions for the final four months (up to the second wet season).
White space within the domain indicates dry cells.
102
CHAPTER 4
MODELING PHOSPHORUS WATER-QUALITY IN THE SOUTHERN INLAND
AND COASTAL SYSTEMS
Introduction
The freshwater Everglades are oligotrophic due to the strong affinity for
phosphorus exhibited by the carbonate substrate underlying the system (de
Kanel & Morse, 1978). The cycling of phosphorus is a complex mix of physical,
chemical, and biological processes (Figure 4-1) that is too complex to describe
based on fundamental physics and chemistry. However, many processes can be
functionally lumped together to simplify and abstract the system of cycling to a
manageable degree of complexity.
The Southern Inland and Coastal Systems (SICS) region encompasses two
principle habitat structures; slough and marl prairie. Taylor Slough, running
southwards through the center of the region (Figure 3-1 in Chapter 3), has
proportionately less emergent macrophyte biomass and more floating
macrophyte and periphyton biomass than adjacent marl prairie, which is a
complex of sawgrass (predominantly) and calcareous periphyton (Swain et al.,
2004). Both systems have significant layers of flocculent material (floc), a loose
conglomerate of bacteria, periphyton and partially decomposed litter (Noe et al.,
2003). Uptake of surface-water phosphorus in both systems is dominated by
periphyton and floc (Noe et al., 2003; Noe and Childers, 2007). Emergent
macrophytes in the marl prairies obtain the majority of their phosphorus from
porewater (Richardson and Marshall, 1986). Floating macrophytes absorb
phosphorus directly from the water column, but turnover is rapid (Mitsch, 1995).
103
In Taylor Slough, periphyton and macrophyte litter accrete and produce
organic soils. The periphyton in the marl prairies co-precipitate phosphorus with
calcium, which accrete to form marl soils. Both forms of soil store phosphorus
and do not readily release it unless conditions become dry (Sutula et al., 2001).
Atmospheric deposition is probably the most important source of nutrients
to the southern Everglades (Noe and Childers, 2007; Sutula et al, 2001). Under
historic conditions atmospheric deposition is estimated to have accounted for up
to 90% of total phosphorus inputs to the Everglades (Davis, 1994). Flow into the
southern Everglades does not generally exhibit the amplified nutrient loading
more prevalent further north, where wetlands receive waters directly from the
EAA.
Ground-water and surface-water in the region are also readily exchanged
because of the combination of shallow topography and particularly high hydraulic
conductivity (Fennema et al., 1994), though the extent to which such exchange
contributes nutrients is unclear. Recently, Price et al. (2006) have suggested
that phosphorus inputs from ground-water may increase during the dry season
due to a reversal of hydraulic gradient that causes upwelling rather than leakage.
Integrated ground-water and surface-water modeling of SICS (Langevin et al.,
2005) have also indicated that there is upwelling during low-flow periods.
However, the effects on productivity that this ground-water input of nutrients is
suggested to drive are found largely in the mangrove/marshland ecotone in the
southern portion of Taylor Slough, and are not thought to be as significant in the
freshwater wetlands that are the focus of this modeling work.
104
Together, these biological, chemical, and physical processes interact to
determine the concentration of phosphorus in the water column, and in turn the
mass exported out of the system. By considering simplified representations of
these processes an abstracted yet functionally mechanistic water-quality model
can be developed that is sufficiently simple to remain manageable and justifiable,
yet sufficiently complex to provide insights into internal biogeochemical
processes that cannot be captured by simple reactive-transport models.
However, such simple models are not without merit, and depending on the
objectives of the modeling exercise may prove sufficient in themselves. We
explore the value of a number of models for the purpose of simulating total
phosphorus concentrations in SICS surface-waters, from the simple reactivetransport model to a more detailed model of conceptualized biogeochemical
cycling.
Materials and Methods
The integrated surface-water flow, transport and reaction simulation engine
that was described in Chapter 2, and applied to model hydrology in in Chapter 3,
was applied to simulate surface-water total phosphorus concentrations in the
SICS region for the period of August 1996 through October 1997. Two locations
were identified with measured total phosphorus concentrations in the surfacewater against which to compare simulated results. These were the P37 and
EPGW hydrologic stations introduced in Chapter 3, and depicted in Figure 4-2.
Boundary Conditions
Concentration boundary conditions were required for each of the surfacewater boundary locations described in Chapter 3 (Figure 4-2). These boundary
105
conditions were associated with either specified head or specified discharge
boundary conditions at the lateral boundaries. Atmospheric deposition of
phosphorus is input to describe the vertical inputs.
Specified water-level boundaries
For boundaries in Florida Bay (specified head boundaries 1 to 4 in Figure 42), time-series data was obtained for relevant water-quality observation stations
in Florida Bay (Table 4-1). These data were interpolated and input into the
SWIFT2D input file as time-varying data. Time-varying concentration data at
specified water-level boundaries are specified in Record 2A of Part 3 of the
SWIFT2D input file (Swain, 2005) at the same time intervals at which timevarying tidal (water-level) boundary conditions are read in. A FORTRAN
program was therefore written to do this efficiently and reliably given the very
large number of required inputs at this interval (see Subroutine EDIT_INPUTFILE
in Appendix C, Section C1).
Time-series data for concentrations at specified head boundaries within the
oligotrophic marsh areas (boundaries 6-8) were not available. However, analysis
of long-term concentration trends at stations situated within oligotrophic
marshlands (EPGW and P37) show that concentrations tend to be either below
detection limit (i.e. less than 4 ppb), or on the order of 5 ppb. Total phosphorus
concentrations well below 10 ppb are common in the Everglades (McCormick et
al., 1996) with any excess phosphorus rapidly taken up (Rudnick et al., 1999).
Given that discharge sources are the dominant lateral hydrologic input and that
measured boundary concentrations are available for these (see below), and
106
considering the known importance of atmospheric deposition, a background
concentration of 5 ppb was considered justifiable.
Specified discharge boundaries
Time-series concentration data for discharge sources were obtained for the
pumping stations used to specify boundary condition flow rates. The TSB
discharge source was specified using pumping data from the Taylor Slough
Bridge site, the L-31W source with data from the S-175 pumping station, and the
C-111 source with data from the S18C pumping station (Swain et al., 2004).
Total phosphorus concentrations for these stations were obtained from the
SFWMD water-quality database, DBHydro (Tables 4-2 to 4-4). Additional data
sets used in a Florida Bay water-quality model (Walker, 1998) were identified that
contained supplementary data for the period of interest (Tables 4-2 to 4-4).
These data sources were consolidated and the time-series data interpolated for
daily input to the water-quality model. Additional code had to be written into
SWIFT2D to handle the addition of total phosphorus mass at the discharge
sources. Mass of phosphorus added to the cell containing the discharge source
was calculated based on the volume discharged and the input concentration. The
mass was then added to the existing mass within the cell and the updated cell
concentration determined, accounting for dilution and concentration effects due
to additions and losses of water, from precipitation and ET, respectively. The
subroutine STRUCTCONCS (see Appendix C, Section C1) was written to read
daily discharge source concentration inputs from a new input file
INPUTFLOWCONCS.dat (see Appendix C, Section C2). For consistency with
the existing methods within SWIFT2D for handling sources of water, including
107
discharge sources, the format of the concentration data input file and its
processing by the STRUCTCONCS subroutine were based on the methods used
for input and handling of water sources.
Atmospheric deposition
A value of 0.03 g TP/m2/yr was chosen given past application of this value
for phosphorus budgets in southern Florida (Sutula et al., 2001 ; Noe and
Childers, 2007). Given the known uncertainty of this input and the system’s
reported sensitivity to it, the sensitivity of the water-quality model to this input was
explored by evaluating three different options for applying this average annual
rate: Option 1) a fixed daily rate of 8.219E-5 g TP/m2/d based on the annual
deposition of 0.03 g TP/m2/yr distributed evenly over 365 days; Option 2) a fixed
rate of 9.709E-5 g TP/m2/d applied only on days on which rain occurred, based
on the annual deposition of 0.03 g TP/m2/yr and the number (309) of rain days;
and Option 3) a rate proportionate to the rainfall volume on each given day,
summing to 0.03 g TP/m2/yr. In this way, mass of phosphorus added to system
in each case was the same.
Conceptual Models of Water-Quality Processes
Wetland biogeochemical processes are extremely complex. It is therefore
necessary to abstract and simplify the many processes into a conceptual model
of manageable and useful complexity. Noe and Childers (2007) have calculated
annual phosphorus budgets for oligotrophic sloughs that contain phosphorus
pools for water, floc, periphyton, soil, consumers, dead aboveground
macrophytes, live aboveground macrophytes, and live macrophyte root biomass.
Such complexity is unjustifiable in this instance given the absence of data against
108
which to compare the simulated results in a spatially heterogeneous and
transient simulation. Furthermore, without data to constrain the many parameters
that describe the flux of phosphorus between so many pools, fluxes that are
themselves often very uncertain estimates (Noe and Childers, 2007; Noe et al.,
2003; Sutula et al., 2001), there is a likelihood of generating non-identifiability
and non-uniqueness issues in such a complex spatially-distributed model due to
overparameterization (Beven, 1992).
Given the adaptable nature of the water-quality functionality in
FTaRSELOADDS, a number of water-quality models (Figures 4-4, 4-5 and 4-6)
were tested with increasingly complex conceptualizations of phosphorus cycling
following the approach adopted in Jawitz et al. (2008) and recommended as
good practice by Chwif et al. (2000).
Model 1
Applying the principle of Occam’s Razor, the most simple case possible
treated total phosphorus as a conservative tracer (Figure 4-4). In this case, the
implicit assumption is that phosphors uptake from the surface-water through the
many processes described in the introduction is balanced with atmospheric
deposition and other internal sources. This is a reasonable assumption given the
efficient uptake of available phosphorus reported for oligotrophic Everglades
wetlands (Davis, 1994; Noe et al., 2001) and the consistently low and relatively
invariant concentrations recorded for the region (McCormick, 1996).
Atmospheric deposition was therefore not added to the water column in this
application, though inputs with lateral flow through the specified head and
concentration boundaries were maintained.
109
Model 2
The second tested model (Figure 4-5) accounted for atmospheric
deposition as a model input, and simulated phosphorus extraction from the
surface-water with a simple first-order sink term, intended to capture the lumped
effect of biotic uptake and physical processes that remove phosphorus from the
water column. This method was used to explore the three atmospheric
deposition options described above. The time-step at which reactions were
applied was that implemented for the transport and hydrology in SWIFT2D, being
1.5 minutes (see Chapter 3). To facilitate comparison, a single uptake rate that
best fit all three methods was determined rather than individual rates for each
case. Manual calibration showed that a rate 1.5E-6 s-1 offered the best result.
Model 3
The most complex case made full use of aRSE to simulate a conceptual
water-quality system of processes including lumped biotic uptake of phosphorus,
senescence, burial, and release of phosphorus from the dead biomass back into
the water column (Figure 4-6).
Although aRSE includes methods to solve partial differential equations
using the Runge-Kutta 4th order solution methods, testing for numerical stability
indicated that a maximum time-step of 15 minutes was permissible. This proved
to be an untenable time-step for computational time considerations.
Alternatively, aRSE offers simple equation solving in two separate steps, known
as “presolve” and “postsolve”. This offered a means of solving the system of
equations at a more reasonable daily time-step using a mass-balance approach.
This was the method adopted.
110
Noe et al. (2003) conducted a radioisotope tracing study to examine the
cycling and partitioning of phoshorus in an oligotrophic Everglades wetland
(Figure 4-7). Peak tracer signals were obtained after 10 days (Noe et al., 2003),
at which point the partitioning of the tracer between what remained in the
surface-water and what had been removed was used to estimate an average
daily uptake rate of 0.084375 day-1.
The measured partitioning of phosphorus in Noe et al. (2003) was applied
to determine rates of uptake by living biomass, considered to be the lumped pool
of macrophytes, all forms of periphyton, consumers, and floc. The observed rate
of flux from living to dead material was used to estimate the senescence rate and
burial rate as a function of the uptake rate (Noe et al., 2003). DeBusk and Reddy
report rates for sawgrass decomposition of 0.00067 to 0.003 d-1. McCormick et
al. (1996) reported aerobic decomposition of periphyton mats ranging from 0.006
go 0.11 d-1, and Newman and Pietro (2001) report periphyton decomposition on
the order of 0.0003 d-1. After calibration a value of 0.001 d-1 was chosen.
Parameters, their values and their sources are presented in Table 4-5.
State-variables, their initial conditions, and their definition in the XML input file
are given in Table 4-6. The full system of equations input to aRSE are given in
the XML input file (XMLINPUT.xml) in Appendix C (Section C3). The IWQ input
file (IWQINPUT.iwq) which contains the definitions of model parameters and their
values for access by SWIFT2D (see Chapter 2) is also given in Appendix C
(Section C3), as well as the SWIFT2D input file (WETLANDS.inp).
111
Results and Discussion
Results for each of the 3 model complexities applied are presented. The
simulation periods were extended beyond the 12-month hydrologic period
presented in Chapter 3 up to mid-October of 1997. In this way an additional
validation data-point for the P37 station was obtained. No such data was
available for the EPGW station until much later (and beyond the maximum
simulation length for this work). Table 4-7 summarizes the Nash-Sutcliffe
efficiencies obtained for each of the models applied.
Model 1
Simulated results for a location in Taylor Slough (P37) and the marl prairies
of the C-111 wetlands (EPGW) for the case of conservative transport are shown
in Figure 4-8. The quality of results indicates the assumption that atmospheric
deposition and internal sources are balanced by internal sinks is justifiable. The
model performed better in the marl prairies (Nash-Sutcliffe of 0.74) than in the
slough environment (Nash-Sutcliffe of 0.58), but the average efficiency of 0.66
implies that conservative transport may be an acceptable approximation for
estimating loadings assuming that the mechanistic hydrodynamics are sufficiently
accurate.
Model 2
Figure 4-9 compares the simulated concentrations achieved at stations P37
and EPGW using Model 2 and the three options for atmospheric input. Option 1
input a fixed daily mass irrespective of weather conditions, Option 2 applied a
fixed mass only on rain-days, and Option 3 applied mass relative to the amount
of rainfall on a given day. All three methods were applied such that total mass
112
added over a year summed to 0.03 g TP/m2/yr to ensure comparable loadings to
the system despite the different methods.
Option 1 was the simplest approach to adding deposition, simply dividing
the annual flux equally over each day. This method provided the best results,
with an average Nash-Sutcliffe across both stations of 0.66. Later efforts to
refine the calibrated value of the uptake rate (1.5E-6 s-1) produced no significant
improvement in results so this value and these results were used as the final
simulation of total phosphorus concentrations for Model 2.
Nash-Sutcliffe efficiencies for Option 2 ranged fro 0.06 to 0.46, which were
poorer than those of the first method, but still reasonable, especially for EPGW.
Nash-Sutcliffe efficiencies for Option 3 were uniformly less than -5 and therefore
unacceptable. Efforts to improve performance by calibrating the rate constant
specifically for this method proved futile because the lag in peaks could not be
shifted through this factor. This method introduced strong spikes and troughs
during periods of sparse rainfall that degraded results in the dry season. The
lack of input given rare rain events and low volume events when rain did occur
lead to significant reductions in concentrations with time. Rainfall events that
then occurred under drier conditions added a disproportionate amount of
phosphorus to low water-level conditions and produced large spikes in
concentration that tended to lag behind the observed values. During wet periods
this problem was mitigated: peaks were not as high due to the diluting effect of
larger volumes of standing water, and troughs were not as low because the
regular input of mass with frequent rainfall kept the mass topped up. By volume-
113
weighting the deposition with rainfall this method implicitly assumes that
deposition is strongly related to rainfall and therefore disproportionately made up
of wet deposition. The failure of this method corroborates the suggested
importance of dry deposition in the SICS region.
Model 3
Results for the most complex model applied are presented in Figure 4-10.
Results for the prairie (Nash-Sutcliffe = 0.73) were comparable in quality to those
obtained using Model 1 (0.74) and better than those obtained with Model 2
(0.70). However, results for the slough environment (Nash-Sutcliffe = 0.23) were
poorer than those obtained using Model 1 (0.58), though comparable to those
obtained with Model 2 (0.28). The average efficiency for both measurement
stations using Model 3 was a respectable 0.47.
As was the case for all the other models, results for the marl prairie station
(EPGW) were noticeably better than those obtained for the slough station (P37).
While it is unclear why this trend should be present for Models 1 and 2, it can be
explained in Model 3 by noting that the radioisotope study conducted by Noe et
al. (2003) was performed in wet prairie marshes in Shark River Slough. The
location of this study within marshes within a slough was originally thought to be
useful because of the presumed aggregating effect of the habitat being a marsh
within a slough, and the fact that SICS is comprised of marsh and slough.
However, given the modeling results it appears that the measured rates were
more appropriate for marsh/wet prairie conditions than for slough conditions, and
this hoped for aggregating effect was not present, or remained biased towards
marsh conditions.
114
Conclusions
Three different models of increasing complexity were applied to the
modeling of phosphorus water-quality in the SICS region. Average NashSutcliffe efficiencies ranged from 0.47 to 0.66, indicating that phosphorus waterquality could be reasonably simulated with multiple models of differing
complexity. Considering this result, the additional complexity inherent to applying
a model akin to Model 3 must be justified by the objectives of the modeling effort
or theoretical considerations pertaining to the underlying conceptual model.
For instance, though the best results were obtained with the simplest
model, this version is subject to the greatest structural uncertainty because of the
sweeping assumptions implicit in its simple form. Model 3 also remains subject to
significant simplifying assumptions, but there is a degree of mechanistic process
to the conceptual model at this higher complexity that imbues the model with
greater theoretical justification. Alternately, if the objectives are to assess how
frequently conditions exceed a specified threshold, say for example the CERPmandated maximum TP concentration of 10 ppb, we see that the more dynamic
results from Model 3 capture multiple exceedence events that were missed by
the simpler versions.
The question of how best to handle the problematic but important input of
atmospheric deposition appears to be best answered with the most simple
solution; an annual average evenly distributed across all days of the year.
Occam’s Razor would tend to support this approach in any event given the great
uncertainties, but the comparison of input methods yielded some valuable
insights into the problem. Despite the conjectured role of convection storms in
115
harvesting phosphorus from the upper atmosphere, and the regularity of rainfall
in the wet season, results indicated the a rainfall volume-weighted approach was
not advisable. The second deposition method, which assumes rainfall captures
and flushes the dry deposits, performed well but not as well as daily average.
This work, however, remains founded on an annual average that is itself subject
to significant uncertainty, and requires further study and experimentation to
assess the full extent of model sensitivity to this source of uncertainty.
The issue of model complexity is an important one in the context of model
development, and the availability of a tool such as FTaRSELOADDS, which
provides the user with the freedom to define and experiment with model structure
demands of the user a greater understanding of the role of complexity on model
performance. Despite the reduced structural uncertainty, additional complexity is
known to also introduce uncertainty into models through the additional
parameters that are needed, each subject to some measurement uncertainty. In
this case, the uncertainty associated with atmospheric deposition may well be the
underlying reason for the simplest model, which neglected to account for
atmospheric deposition, performing the best. Any effort to mechanistically model
water-quality in the oligotrophic Everglades is surely going to be greatly
hampered using such uncertain measures for such an important input.
Further complexity could be introduced into the water-quality model to
produce more biogeochemically detailed models, and these may well improve
results despite the uncertainty of deposition, but such an effort needs to be
constrained with sufficient data to prevent sensitivity in the model from
116
undermining the integrity of calibration. The paucity of phosphorus data against
which to evaluate model performance in this period is a challenge, though more
recent research in the region of Taylor Slough (Childers, 2006) has produced
much data that would probably be sufficient to test greater complexity. The
following chapter will explore the issue of model complexity, uncertainty and
sensitivity in greater detail.
As discussed in Swain et al. (2004), accurate capture of flow reversals in
the tidal creeks is largely due to wind driven effects and not simply tidal
fluctuations. The importance of wind-shear in this environment has implications
for wind-induced mixing effects in the transport solution that cannot be captured
by hydrologic models that do not account for this hydrodynamic effect. It is
therefore quite possible that the good results obtained in all models, but
particularly the conservative transport approach, would be eroded were a less
hydrodynamic model simulating the transport. This would require further testing
to confirm given that both phosphorus observation stations are located some
distance from the tidal creeks where this effect is most prominent.
117
Table 4-1. Stations and total phosphorus concentration data (g/m3) used for
interpolation of daily concentrations for specified head boundary
conditions in Florida Bay. Station numbers correspond with those of
Figure YY and boundary condition numbers with those of Figure XY.
3
Date
TP [g/m ]
TP [g/m ]
3
TP [g/m ]
3
TP [g/m ]
3
TP [g/m ]
3
TP [g/m ]
3
Station 3
Station 6
Station 13
Station 15
Station 23
Station 24
7/4/96
8/21/96
9/13/96
0.00597
0.00566
0.00698
0.00822
0.00628
0.00698
0.01108
0.01651
0.02077
0.01256
0.03294
0.01333
0.00481
0.00760
0.00465
0.00411
0.00395
0.00349
10/14/96
11/8/96
12/5/96
0.00612
0.00411
0.00496
0.00806
0.00806
0.00581
0.01992
0.00891
0.00736
0.03216
0.01201
0.01744
0.00581
0.00457
0.00527
0.00558
0.00434
0.00527
1/7/97
2/14/97
3/13/97
4/15/97
5/23/97
6/11/97
7/9/97
8/20/97
9/9/97
10/22/97
11/24/97
12/11/97
BC no.
0.00419
0.00512
0.00496
0.00535
0.00581
0.00605
0.00411
0.00481
0.00380
0.00349
0.01604
0.00636
0.00667
0.00884
0.00752
0.00868
0.00798
0.00822
0.00860
0.00512
0.00581
0.00930
0.00915
0.00977
BC 4**
0.01116
0.02534
0.00891
0.00783
0.00845
0.01015
0.02255
0.02108
0.02093
0.01643
0.01232
0.01256
BC 2
0.01620
0.01767
0.01240
0.01380
0.00907
0.01116
0.02612
0.02860
0.02031
0.03534
0.01759
0.01411
BC 1
0.00388
0.00349
0.00388
0.00473
0.00450
0.00558
0.00349
0.00186
0.00264
0.00271
0.00473
0.00473
0.00767
0.00550
0.00690
0.00837
0.00535
0.00605
0.00729
0.00620
0.00628
0.00496
0.00682
0.00558
BC 3***
* Data provided by the Southeast Environmental Research Center monitoring
program in Florida Bay (http://serc.fiu.edu/wqmnetwork/SFWMDCD/Pages/FB.htm)
** Applied the average of station 3 and station 6
*** Applied the average of station 23 and station 24
118
Table 4-2. Data sources and values used for boundary conditions concentrations
at the L-31W discharge source
S175: From DBHYDRO
S175: From Walker
(SFWMD)
(1998)
Averaging per month**
Date
TP [ppm]
Date
TP [ppm] Date
TP [ppm]
7/11/96
0.0090
7/96
0.0034
7/96
0.0062
7/24/96
BDL
8/7/96
BDL
8/96
0.0031
8/96
0.0031
8/20/96
BDL
9/11/96
0.0040
9/96
0.0039
9/96
0.0040
9/24/96
BDL
10/9/96
0.0080
10/96
0.0050
10/96
0.0065
10/22/96
BDL
11/6/96
BDL
11/96
0.0033
11/96
0.0033
11/19/96
BDL
12/4/96
0.0070
12/96
BDL
12/96
0.0070
12/17/96
BDL
1/8/97
0.0040
1/97
BDL
1/97
0.0055
1/21/97
0.0070
2/12/97
0.0040
2/97
BDL
2/97
0.0040
3/12/97
BDL
3/97
BDL
3/97
0.0040
--4/97
BDL
4/97
0.0040
5/21/97
BDL
5/97
0.0084
5/97
0.0062
6/12/97
0.0090
6/97
0.0084
6/97
0.0071
6/25/97
0.0040
7/8/97
BDL
7/97
0.0035
7/97
0.0043
7/22/97
0.0050
8/5/97
BDL
8/97
0.0063
8/97
0.0052
9/2/97
0.0040
9/17/97
0.0064
9/97
0.0050
9/97
0.0051
9/30/97
BDL
Annual mean
0.0061*
0.0050*
0.0050
BDL="below detection limit"
* Excluding BDL
** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the
assumed detection limit of 0.004 ppm was included in the average. If no data
was recorded by SFWMD then the Walker (1998) value was used. If only BDL
records existed then 0.004 ppm was used.
-- No data sampled by SFWMD that month
119
Table 4-3. Data sources and values used for boundary conditions concentrations
at the C-111 discharge source.
S18C: From DBHYDRO
S18C: From Walker
(SFWMD)
(1998)
Averaging per month**
Date
TP [ppm]
Date
TP [ppm] Date
TP [ppm]
7/11/96
BDL
7/96
0.0030
7/96
0.0030
7/24/96
BDL
8/7/96
BDL
8/96
0.0032
8/96
0.0032
8/20/96
BDL
9/11/96
0.0040
9/96
0.0035
9/96
0.0038
9/24/96
BDL
10/9/96
0.0040
10/96
0.0034
10/96
0.0037
10/22/96
BDL
11/6/96
BDL
11/96
0.0040
11/96
0.0045
11/19/96
0.0050
12/4/96
0.0040
12/96
0.0038
12/96
0.0039
12/17/96
BDL
1/8/97
0.0050
1/97
0.0041
1/97
0.0044
1/21/97
0.0040
2/12/97
BDL
2/97
0.0031
2/97
0.0031
3/12/97
BDL
3/97
0.0033
3/97
0.0033
--4/97
0.0068
4/97
0.0068
--5/97
0.0115
5/97
0.0115
6/12/97
0.0290
6/97
0.0214
6/97
0.0185
6/25/97
0.0050
7/8/97
BDL
7/97
0.0031
7/97
0.0031
7/22/97
BDL
8/5/97
BDL
8/97
0.0063
8/97
0.0052
09/2/97
0.0041
9/97
0.0046
9/97
0.0046
09/17/97
0.0051
Annual mean
0.0075*
0.0058
0.0056
BDL="below detection limit"
* Excluding BDL
** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the
assumed detection limit of 0.004 ppm was included in the average. If no data
was recorded by SFWMD then the Walker (1998) value was used. If only BDL
records existed then 0.004 ppm was used.
-- No data sampled by SFWMD that month.
120
Table 4-4. Data sources and values used for boundary conditions concentrations
at the TSB discharge source.
TSB: From DBHYDRO
TSB: From Walker
(SFWMD)
(1998)
Averaging per month**
Date
TP [ppm]
Date
TP [ppm] Date
TP [ppm]
7/9/96
BDL
7/96
0.0047
7/96
0.0044
8/6/96
0.0120
8/96
0.0081
8/96
0.0101
9/10/96
0.0040
9/96
0.0041
9/96
0.0041
10/15/96
BDL
10/96
0.0031
10/96
0.0031
11/5/96
BDL
11/96
0.0045
11/96
0.0043
12/3/96
0.016
12/96
0.0152
12/96
0.0156
--1/97
0.0138
1/97
0.0138
--2/97
BDL
2/97
0.0040
--3/97
0.0058
3/97
0.0058
--4/97
0.0081
4/97
0.0081
--5/97
0.0067
5/97
0.0067
6/24/97
BDL
6/97
0.0040
6/97
0.0040
7/29/97
BDL
7/97
0.0030
7/97
0.0030
8/19/97
BDL
8/97
0.0029
8/97
0.0029
09/16/97
BDL
8/97
0.0035
8/97
0.0035
Annual mean
0.0107*
0.0063*
0.0062
BDL="below detection limit"
* Excluding BDL
** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the
assumed detection limit of 0.004 ppm was included in the average. If no data
was recorded by SFWMD then the Walker (1998) value was used. If only BDL
records existed then 0.004 ppm was used.
-- No data sampled by SFWMD that month.
121
Table 4-5. Parameters used in the model
Parameter Definition
XML input
Value
Units
Source
Noe et al.,
2003
ku
P uptake rate
k_uptake
0.083475
d-1
ksn
Senescence
rate as a
function of
uptake
k_senesc
0.25
--
Noe et al.,
2003
0.001
d-1
Calibration;
Debusk and
Reddy,
2005;
Newman et
al.; 2001
0.13
--
Noe et al.,
2003
kdc
Decomposition
rate
kb
Burial rate as a
function of
k_soil
uptake
k_decomp
From
SWIFT2D
Kw
Wet/dry factor
K_wet
1 or 0
-based on
ICLSTAT*
* ICLSTAT(N,M) is 0 if a cell is considered wet at the time by SWIFT2D, or >0 if
dry.
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Table 4-6. State-variables with initial conditions
State
variable
Definition
XML input
(Figure 4-6)
TP
concentration
[TPsw]
TP_sw_conc
in the surfacewater at t
Mass of TP in
the surfaceTP_sw_mass1
water at t-1
TPsw
Mass of TP in
the surfaceTP_sw_mass2
water at t
TP uptake
from the
TP_uptake1
surface-water
for t
TPu
TP uptake
from the
TP_uptake2
surface-water
for t-1
TP in live
biomass at
TP_live1
time t
TPbio
TP in live
TP_live2
biomass at
time t-1
TP in dead
biomass at
TP_dead1
time t
TPdead
TP in dead
biomass at
TP_dead2
time t-1
TP flux by
TPsn
senescence at TP_senesc
time t
TP flux by
TPdc
decomposition TP_decomp
at time t
TP flux by
TPb
TP_bury
burial at time t
TP in the soil
TP_soil1
at time t
TPs
TP in the soil
TP_soil2
at time t-1
123
as used in Model 3
Initial
condition
Units
(aRSE)
0.005
g TP/m3
0.01
g TP/m2
0.01
g TP/m2
0.0008
g TP/m2/d
0.0008
g TP/m2/d
0.04
g TP/m2
0.04
g TP/m2
0.014
g TP/m2
0.014
g TP/m2
0.0002
g TP/m2/d
0.0001
g TP/m2/d
0
g TP/m2/d
0.0001
g TP/m2
0.0001
g TP/m2
Table 4-7. Nash-Sutcliffe efficiencies for the water-quality models applied to
simulate total phosphorus in the Southern Inland and Coastal Systems
Model 2
Model 2
Model 2
Model1
Model 3
(Option 1)
(Option 2)
(Option 3)
P37
0.583531
0.285041
0.062226 -5.183816
0.226110
EPGW
0.737771
0.697249
0.460871 -5.612662
0.733882
Combined
0.658693
0.484382
0.255956 -5.364559
0.471255
124
Figure 4-1. Schematic of phosphorus cycling processes in Everglades wetlands.
125
7
5
9
8
10
11
6
P37
EPGW
4
1
2
3
Figure 4-2. Location of SICS model boundary conditions including specified head
boundaries (blue), discharge sources (orange), and the associated total
phosphorus concentration boundary conditions (black – squares indicate
specified head and circles discharge sources; numeric references refer to
Table 4-1) at each of these (map and hydrologic boundaries from Swain et
al., 2004).
126
Figure 4-3. Location of water-quality observation points in Florida Bay. Data are
provided by the Southeast Environmental Research Center
(http://serc.fiu.edu/wqmnetwork/SFWMD-CD/Pages/FB.htm)
127
Figure 4-4. Model 1: Conservative transport assuming deposition and internal sources
are in equilibrium with biotic uptake and internal sinks. Green fill indicates
total phosphorus, and blue lines indicate the medium is water.
128
Figure 4-5,. Model 2: First-order uptake from the water column using the reactive
transport functionality of SWIFT2D (Model 2a) or aRSE for reactions and
SWIFT2D for transport (Model 2b).
129
Figure 4-6. Model 3: Reactions simulated by aRSE with transport by SWIFT2D. For
XML equations see Appendix C (Section C3). Variables and parameters
defined in Tables 4-5 and 4-6.
130
Figure 4-7. Mean proportion of total recovered radioisotope (32P) per mesocosm found
in different ecosystem components over time (from Noe et al., 2003).
131
Figure 4-8. Simulated TP concentrations obtained with Model 1 at observation stations
in Taylor Slough (P37) and C-111 wetlands (EPGW).
132
Figure 4-9. Simulated TP concentrations obtained with Model 2 for each of the
atmospheric deposition options explored at observation stations in Taylor
Slough (P37) and C-111 wetlands (EPGW).
133
Figure 4-10. Simulated TP concentrations obtained with Model 3 at observation stations
in Taylor Slough (P37) and C-111 wetlands (EPGW).
134
CHAPTER 5
UNRAVELING MODEL RELEVANCE: THE COMPLEXITY-UNCERTAINTYSENSITIVITY TRILEMMA
Introduction
At its heart, our inability to truly simulate environmental (open) systems (Oreskes
et al., 1994; Konikow and Bredehoeft, 1992) is due to our inability to reproduce their
complexity. There are many reasons for this shortcoming: a lack of understanding in
poorly studied systems or the inability to either conceptualize or reproduce the
intricacies of well-studied systems; the inability of our instruments and methods to
obtain true observations needed for parameterization and calibration due to
measurement uncertainties and heterogeneities in space and time and scale; and the
discontinuous nature of numerical solutions that imperfectly reproduce the continuity of
reality. Such limitations prohibit true model validation (Oreskes et al., 1994). In lieu of
confirming such validity, we strive instead for confidence in model results, which we
consider by evaluating the extent of our doubt, as indicated by the degree of uncertainty
associated with the generated results (Naylor and Finger,1967; Beven, 2006a). There
is growing unease among developers and users of dynamic simulation models about
the cumulative effects of various sources of uncertainty on model outputs, which inherit
these underlying uncertainties (Manson, 2007 and 2008; Cressie et al., 2009; Messina
et al., 2008). In particular, this issue has prompted doubt over whether the considerable
effort going into further elaborating complex dynamic system modeling will in fact yield
the expected payback, viz. new insights about the complicated systems they are
intended to simulate (Ascough et al., 2008). The concern is that insufficient heed has
been paid to the balance between investment (complexity) and return (uncertainty),
135
which was succinctly captured by Zadeh (1973), who first presented the notion of
relevance as part of his “principle of incompatibility”:
... the conventional quantitative techniques of system analysis are
intrinsically unsuited for dealing with humanistic systems or, for that matter,
any system whose complexity [emphasis added] is comparable to that of
humanistic systems [author’s note: e.g. environmental systems]. The basis
for this contention rests on what might be called the "principle of
incompatibility". Stated informally, the essence of this principle is that as
the complexity of a system increases, our ability to make precise and yet
significant statements about its behavior diminishes until a threshold is
reached beyond which precision and significance (or relevance [emphasis
added]) become almost mutually exclusive characteristics.
The relevance of a model is contingent on the balance between its power to
address questions and the power of its answers. The former is dependent on model
complexity – the degree of detail to which the real system is reproduced in the model
structure. The latter is dependent on model uncertainty – the accuracy, precision and
confidence associated with output results. Our failure to attend more closely to this
balance is due largely to insufficient understanding of how complex models gain and
lose relevance. Failure to advance this understanding has been at least in part due to
the practical limitations associated with complex models. In particular, mechanistic
environmental models are among the most complex, demanding specialized numerical
code of spatially-distributed domains, numerous state variables, and a plethora of input
parameters and data. Such complex tools are typically developed by specialists and,
once complete, are not very amenable to adjustments in structure. The choice of
complexity in such tools has therefore more commonly been the responsibility of model
developers, while users simply have to deal with the consequences. Users do have a
choice between potential tools of differing complexity, but that decision is still based on
fixed choices, and is generally the product of a multitude of other considerations that
136
comprise what most modelers understand as the “art of modeling” (Getz, 1998;
Basmadjian, 1999). We believe that suitable tools now exist to support controlled
experimentation with model complexity, as well as more rigorous investigation into the
consequences for uncertainty. Using such tools, we propose and demonstrate that
meaningful new progress can be achieved toward unraveling the issue of relevance.
The Complexity-Uncertainty-Sensitivity Trilemma
To this point, we have used the term “uncertainty” to encompass various types of
uncertainty, some quantifiable and some less so, which collectively contribute to the
epistemic uncertainty in model results (that is, uncertainty associated with our
knowledge about the state of a simulated system; Regan et al., 2002). To better
investigate total epistemic uncertainty, it becomes necessary to distinguish between
specific forms of uncertainty. The most commonly encountered form of uncertainty in
modeling is error, which is a measure of model accuracy (i.e., the discrepancy between
simulated results and observed data). Another prevalent form of uncertainty is that due
to the uncertainties inherent to the values of input parameters, which are propagated
through a model and onto the outputs and manifest as precision (i.e., the irreducible
uncertainty in any model result that determines the range of possible values the actual
result might inhabit). This is the sense of the word most commonly intended in the
context of uncertainty analysis, and is the meaning adopted in all following sections
unless specified otherwise. Other forms of uncertainty exist, most of which are difficult
to assess because they are conceptually more qualitative, for example: uncertainty due
to the underlying assumptions and structure of a model; uncertainty in the interpretation
of voluminous and complicated results; and uncertainty in the validity of a model’s
calibration due to model sensitivity. All are influenced by model complexity, but
137
sensitivity is particularly interesting in the context of investigating relevance. Methods of
sensitivity analysis now exist to rigorously quantify sensitivity in such a way as to not
only characterize the flexibility inherent to the model, and thereby the risk of
overparameterization issues, but also to illuminate how the sensitivity is caused and
possible ways for improving the precision of results (Saltelli et al., 2004). This
feedback, linking sensitivity and uncertainty, completes a tripartite dialectic between
complexity, uncertainty, and sensitivity – the relevance trilemma that guides this work.
Uncertainty
There is growing interest in evaluating the contributions of model inputs
(uncertainty in data) and model structure (uncertainty from the simplifying assumptions
necessary to abstract reality into model design and algorithms) to the overall uncertainty
of model outputs (Beven and Binley, 1992; Beven, 1993; Draper, 1995; Cressie et al.,
2009). However, the sources and magnitude of uncertainty and their effect on dynamic
model outputs have not been comprehensively studied (Haan et al., 1995; Beven,
2006a; Shirmohammadi et al., 2006; Muñoz-Carpena et al., 2007; Valle et al., 2009).
Uncertainty analyses endeavor to address this by propagating the various uncertainties
onto a model output, and many methods exist to achieve this end (Haan, 1989;
Shirmohammadi et al., 2006; Cressie et al., 2009). Systems that are better described
and characterized (as physical systems such as hydrology tend to be) are more suitable
for variance-based methods that apply Monte-Carlo simulations, such as the
Generalized Likelihood Uncertainty Estimation method (GLUE; Beven and Binley,
1992). However, many systems (such as ecosystems) are poorly understood and
modeler experience and subjectivity play an important role in their simulation.
Uncertainty assessments that employ Bayesian methods are better suited to
138
incorporate subjectivities and are therefore often favored in such circumstances
(Cressie et al., 2009). Merely quantifying the uncertainty in model outputs is insufficient
to fully understand where and how the uncertainty is propagated or to understand the
role of complexity. Sensitivity analysis can be used to determine how uncertainty in
model outputs is apportioned to different sources of uncertainty in the model inputs
(Saltelli et al., 2008). Whereas uncertainty analysis quantifies the overall uncertainty,
sensitivity analysis identifies the key contributors to uncertainty; together they constitute
a reliability assessment of a model (Scott, 1996).
Sensitivity
The sensitivity of a model output to a given input parameter has traditionally been
expressed in terms of the derivative of the model output with respect to the input
variation (Haan et al., 1995; Cariboni et al., 2007). Such sensitivity measurements are
"local" because they are fixed to a point or narrow range where the derivative is taken.
Local sensitivity indices are generally classified as "one-at-a-time" (OAT) methods,
because they quantify the effect of varying a single parameter by altering only its value
while holding all others fixed. Local OAT sensitivity indices are effective only if all
factors in a model produce linear, direct responses in the output, or interest is in the
model response under specific conditions (Saltelli et al., 2004). However, if changes
produced in an output are non-linear, or parameters exhibit interaction effects on model
output response, or an extensible assessment of sensitivity patterns is required, then a
global sensitivity approach is needed (Leamer, 1990; Saltelli et al., 2004). Global
sensitivity analyses (GSA) simultaneously vary all inputs and explore the entire
parametric space of a model, thereby making no assumptions about linearity, additivity,
or monotonicity. In complex models, the output response is often non-linear and non139
additive, so local OAT techniques are not appropriate, and global techniques should be
used (Saltelli et al., 2004). Different GSA methods can be selected based on the
objective and context of the analysis (Saltelli et al., 2000 and 2004; Cacuci, 2003).
Output sensitivity is inextricably tied to uncertainty, representing as it does the
“paths of greatest influence” on the output (those parameters to which the output is
most sensitive). An alternative perspective is that sensitivity represents the “paths of
least resistance” through which input uncertainty will be propagated onto outputs during
an uncertainty analysis. Sensitivity therefore plays an important role in another source
of epistemic uncertainty: model overparameterization, which is variously captured in
both forward and inverse solutions as non-identifiability, non-uniqueness, and
equifinality (Brun et al., 2001; Omlin et al., 2001; Beven, 2006b; Ebel and Loague,
2006). Overparameterization issues are the result of too many degrees of freedom in a
model due to the number of variable parameters. Each additional parameter introduces
an additional source of influence over model outputs. This effect accumulates and can
result in excessive flexibility in the model, which is counterproductive to
parameterization and calibration efforts and can produce poorly defined calibrations or
multiple irresolvable model characterizations (Beven, 2006a).
A poorly calibrated model, or one with a number of calibrated states that may be
physically irreconcilable, undermines confidence in the model’s projections. GSA
methods uniquely capture the internal model relationships between input and output, as
well as between different inputs. These can be used as indicators of a model’s
flexibility, and thereby the risk of non-identifiability and other overparameterization
issues (Snowling and Kramer, 2001). Though it is an important and neglected (Luo et
140
al., 2009) source of epistemic uncertainty, sensitivity quantified in this form remains a
qualitative measure of uncertainty. However, we can surmise that given sufficient
complexity, uncertainty associated with a model’s total sensitivity might be expected to
reach a point that inhibits the model’s relevance, overwhelming any gains in accuracy
from added complexity in analogous fashion to Hanna’s (1998) usual uncertainty
suspects (Figure 5-2). The sensitivity of outputs to interactions between parameters is
a key contributor to overparameterization, and total sensitivity measures that capture
this effect are therefore a useful proxy for assessing the risk over over-sensitivity. By
contrast, greater direct sensitivity implies stronger direct links between input and output,
which is not only less likely to generate overparameterized conditions, but is also
necessary for identifiability (Brun et al., 2001).
Complexity
Model complexity has proved challenging to quantify, or even define (Chwif et al.,
2000). In a sense, complexity remains an abstract quality that can be assessed
according to many factors, with no single definition proving useful for all contexts.
However, when considering the structural complexity of a model, the number of
parameters is generally considered a useful indication of relative complexity, since the
number of parameters is tied to the number of processes included (Fisher et al., 2002).
Incorporating the complexity of the equations themselves can be achieved using a
Petersen matrix, which accounts for the number of mathematical operations (Snowling
and Kramer, 2001). Subjective allocation of complexity “levels” can also be assigned
based on users’ knowledge of the number and nature of the processes included
(Lindenschmidt et al., 2006). In this work, a simple measure of relative complexity is
141
sufficient, and thus distinct complexity levels were defined according to the number of
parameters required.
Given the limitations inherent to simulating reality with simplified tools, it is not
surprising that more complex models are pursued (Arthur, 1999; Beck, 1987). Models
that are too simple may not capture important processes and cannot be proven to
reproduce the measured data for the correct reasons (Nihoul, 1994). The complexity of
a model fundamentally defines (and limits) the potential realities that can be
reproduced. Environmental systems are particularly challenging to simulate, not only
because they contain profound numbers of processes and constituents, but also
because they can shift between alternate stable states, a complex emergent process
(Scheffer, 2009). Such shifts can fundamentally change the nature of a system (i.e., the
shift from an aquatic system dominated by algae to one dominated by macrophytes).
Models that simulate ecological or biogeochemical systems like these within a
physically dynamic environment, such as a hydrodynamic aquatic environment, are
already highly complex. Yet, as we will show, failure to incorporate sufficient
(additional) complexity can have important consequences for a model’s ability to resolve
certain simulated conditions.
The growing interest in optimizing model complexity relative to uncertainty (Cox et
al., 2006; Lawrie and Hearne, 2007) is particularly pertinent today because of the
growing availability of adaptable computational modeling tools, which give the user the
freedom to define model structure, and thus complexity. Dynamic systems that can be
conceptualized without a spatial domain have had such adaptable tools for many years,
with systems such as STELLA finding application in a wide array of fields (Doerr, 1996).
142
Similar versatility has been pursued with GIS modeling tools (e.g., Wesseling et al.,
1996). However, for the case of mechanistic, numerical models of complex
environmental systems, with large, spatially-distributed domains and numerous state
variables, the degree of model complexity has remained largely imposed on model
users.
Nonetheless, the value and amount of specialist time required for such model
development; the dramatic advances in computing capacity (Schaller, 1997) and data
acquisition by remote sensing (Pohl & Van Genderen, 1998); and the economics of
computer code reusability have compelled continued evolution of even the most
complex models toward greater adaptability. Recently, Jawitz et al. (2008) developed a
spatially-distributed numerical water-quality model, the Transport and Reactions
Simulation Engine (TaRSE), with user-definable state variables and biogeochemical
processes. To the authors’ knowledge, this degree of control is novel in such a complex
environmental model. Another driver of increased interest in the effects of model
complexity is the development of multi-disciplinary integrated models that combine
environmental and socio-economic drivers, sometimes through coupling of existing
specialty models into a multi-modeling framework that can incorporate larger uncertainty
than conventional models (Lindenschmidt et al., 2007).
Relevance dilemmas
Previous work has sought to begin the process of elucidating the relationships
between complexity and various forms of epistemic uncertainty. Model complexity has
been long recognized as having important consequences for output uncertainty. Hanna
(1998) illustrated (Figure 5-1a) that increasing complexity by incorporating more state
variables and processes can initially reduce uncertainty, but can have the opposite
143
effect after a certain critical point (Fisher et al., 2002). Greater complexity improves a
model’s conceptual rendition of reality, meaning the model has fewer simplifying
assumptions and therefore less structural uncertainty. However, each additional
process requires parameters to characterize the mathematics, and the uncertainty
associated with each of these accumulates, eventually exceeding any gains. This
makes identification of a potential “inflection point” important, for it reveals the optimal
degree of complexity for modeling a system that incorporates sufficient detail to gain
information while avoiding greater uncertainty and loss of relevance.
Snowling and Kramer (2001) proposed general relationships relating complexity
and two forms of uncertainty: error and sensitivity (Figure 5-1b). The authors showed
that as complexity was increased, model error decreased while model sensitivity
increased. Snowling and Kramer based their hypothesis on the general concept that
reduced structural error increased accuracy in analogous fashion to the reduction of
uncertainty presented by Hanna. Conversely, sensitivity would increase because the
additional parameters required to simulate the additional processes have some effect
on the model outputs, and therefore represent additional degrees of freedom.
This hypothesis has since been supported by work in Lindenschmidt (2006) and
Lindenschmidt et al. (2006). However, all corroborating results presented thus far
(Snowling and Kramer, 2001; Lindenschmidt, 2006; Lindenshcmidt et al., 2006) are
subject to limitations in generality, having been produced for limited ranges of
parameter variation, centralized around calibrated applications, or based on local OAT
sensitivity analyses. Furthermore, existing support for this hypothesis does not address
how the nature of sensitivity changes with model complexity. Improving our
144
understanding of these dilemmas, between complexity and uncertainty, complexity and
error, and complexity and sensitivity, is crucial to improving our understanding of
relevance. However, it is also necessary that we acknowledge the links between such
dilemmas, which further complicate the problem but cannot be ignored is we wish to
address it. To this end we propose a trilemma, relating complexity, uncertainty, and
sensitivity, as the first step toward a more integrated assessment of relevance.
The relevance trilemma
In this paper we propose the following relationships relating uncertainty, sensitivity,
and model complexity, which together we believe represent a useful characterization for
model relevance (Figure 5-2): 1) Total global sensitivity, being the net sum of all input
effects on an output, increases with complexity due to the additive influence of
additional parameters; 2) Interactions increase with increasing complexity (for the same
reason), and will diminish the role of direct sensitivity as progressively more parameters
interact to control the output and detract from the direct influence of individual
parameters.
To test these hypotheses, we integrated a step-wise model-building approach
using TaRSE, GSA and UA to investigate the role of complexity, and to better guide
development across multiple levels of model complexity. Given doubt associated with
model input factors, such as structural complexity and uncertainty input parameters,
model development that is closely coupled to GSA and UA can reveal important
unintended effects, not only in terms of model sensitivity and uncertainty, but also the
capacity of a model to reproduce real, and complicated, system responses.
145
Materials and Methods
Global Sensitivity and Uncertainty Analysis Methods
Two state-of-the-art global sensitivity and uncertainty methods were used in this
analysis: the qualitative method of Morris (1991) and a quantitative, variance-based
method called the extended Fourier Amplitude Sensitivity Test (FAST; Saltelli, 1999). A
brief summary of each method is given below (further details summarized by MuñozCarpena et al. (2007), and an in-depth treatment of the methods is provided in Saltelli et
al., 2004).
The Morris (1991) method, extended by Campolongo and Saltelli (1997), is
intended to elucidate qualitative global sensitivity, sacrificing quantification in lieu of
dramatically improved computational demands. This method is therefore suitable for
assessing the relative importance of input parameters, and for this reason it is an
efficient screening method often used to filter out unimportant parameters before
conducting the more computationally intensive, and quantitative, FAST analysis (Jawitz
et al. 2008; Saltelli et al., 2005). The Morris method applies a frugal sampling technique
to obtain unique sets of parameter values by varying each within their prescribed range
and probability distribution. The multiple simulations then performed using these unique
sets produce “elementary effects” in the outputs, attributable to changes in each input
parameter, the absolute values of which are averaged to produce a qualitative global
sensitivity statistic, μ*. The magnitude of μ* indicates the relative order of importance
for each parameter with respect to the model output of interest (Campolongo et al.,
2007). The standard deviation of the elementary effects, σ, can be used as a statistic
indicating the extent of interactions between inputs. A higher σ implies variability in the
elementary effects attributed to a particular parameter. Since the values of all other
146
tested parameters are simultaneously varied, this variability implies that the observed
effect is dependent on the values held by other varied parameters (the parametric
context), and thus interaction effects between them. Conversely, an invariant μ* implies
that interactions between parameters do not affect the parameter’s influence on the
output, and that the output is therefore directly sensitive to it. For each output of
interest, pairs of (μ*i, σi) for each input parameter can be plotted in a Cartesian plane to
indicate the relative importance of each output (distance from the origin on the X-axis),
and the prevalence of interaction effects (distance from the origin on the Y-axis).
The variance-based extended FAST method provides a quantitative measure of
the direct sensitivity of a model output to each parameter, using what is termed a firstorder sensitivity index, Si, defined as the fraction of the total output variance attributable
to a single input parameter (i). In the rare case of an additive model, where the total
output variance is explained as a summation of individual variances introduced by
varying each parameter alone, ΣSi = 1. Such additivity is a requisite condition if local
sensitivity analysis results are to be generally applied to a model (Saltelli et al., 2004).
Given that even relatively simple models rarely meet this requirement, the application of
global sensitivity methods should be the preferred approach. In addition to the
calculation of first-order indices, the extended FAST method (Saltelli, 1999) calculates
the sum of the first- and all higher-order indices for a given input parameter (i), called
the total sensitivity index (STi), (Equation 5-1),
STi = Si + Sij + Sijk ... + Si ...n ,
(5-1)
147
where Si is the first-order (direct) sensitivity, Sij is the second-order indirect sensitivity
due to interactions between parameters i and j, Sijk the third-order effects to due to
interactions between i and k via j, and so forth to the final varied parameter, n.
Based on Equation 5-1, total interaction effects can then be determined by
calculating STi - Si . It is interesting to note that μ* of the Morris (1991) method is a close
estimate to the total sensitivity index (STi) (Campolongo et al., 2007). Since the
extended FAST method applies a randomized sampling procedure, it provides an
extensive set of outputs that can then be used in the global uncertainty analysis of the
model. Thus, probability distribution functions (PDFs), cumulative probability
distribution functions (CDFs), and percentile statistics can be derived for each output of
interest with no further simulations required.
In general, the analysis procedure followed six main steps: (1) PDFs were
constructed for uncertain input parameters; (2) input sets were generated by sampling
the multivariate input distribution according to the selected global method; (3) model
simulations were executed for each input set; (4) global sensitivity analysis was
performed according to first the Morris method and then 5) the extended FAST method;
and (6) uncertainty was assessed based on the outputs from the extended FAST
simulations by constructing PDFs and statistics of calculated uncertainty. The free
software Simlab (Saltelli et al., 2004; http://simlab.jrc.ec.europa.eu/) was used for
multivariate sampling of the input parameters and post-processing of the model outputs.
Sample sets were created for all the parameters in each of the complexity levels tested
(see subsequent section and Figure 5-3) and for both methods, resulting in a total of six
sets of analyses. The number of model runs was selected based on the number of
148
parameters in each complexity level according to Saltelli et al. (2004). A total of 1,170
simulations were conducted for the Morris method and 45,046 simulations for the
extended FAST method.
Model Description, Application, and Selection of Complexity Levels
Model description: TaRSE
A water-quality numerical modeling framework, the Transport and Reactions
Simulation Engine (TaRSE), has been developed to simulate the biogeochemistry and
transport of phosphorus in the Everglades wetlands of south Florida (Jawitz et al., 2008;
James et al., 2009). The US$10 billion Comprehensive Everglades Restoration Plan
(CERP) is the largest ecosystem restoration effort in the world, and aims to restore
historic flows and P levels to the ecosystem. The freshwater wetlands of the
Everglades have evolved under phosphorus-scarce nutrient conditions and are
especially sensitive to labile phosphorus in the surface-water (Munsen et al., 2002; Noe
et al., 2003). An important component of CERP therefore entails modeling the waterquality with respect to phosphorus levels, and TaRSE was developed to meet this need.
The design of TaRSE is comprised of two functional modules; one that simulates
the advective and dispersive movement of solutes and suspended particulates in
flowing water (the “Transport” module; James et al., 2009), and one that simulates the
transfer and transformation of phosphorus between biogeochemical components (the
“Reactions” module) (Jawitz et al., 2008). The term “Simulation Engine” refers to the
generic nature of the reactions module, which has been designed such that the user is
responsible for specifying (in XML input files) the model’s state variables and the
equations relating them. State variables cam be grouped in conceptual stores, such as
surface-water or soil, and are classified as “mobile” if they are to be transported or
149
“stabile” if they are not. Thus, even though the inaugural implementation of TaRSE was
intended for phosphorus-related water-quality modeling, this variable structure means it
can be easily adapted for different applications. The user selects from a suite of
equations to describe exchanges between state variables, including zeroth-order, firstorder, Michelis-Mentin growth and decay, sorption-desorption kinetics and rule-based
relations (Jawitz et al., 2008). When applied in a hydrodynamic environment, TaRSE
requires that necessary hydrologic state variables, such as stage and velocity, be
provided by a coupled hydrologic model. TaRSE employs a triangular mesh to
discretize the spatial domain for the Godunov-mixed finite element transport algorithm
(James, et el., 2009), but the reactions module is independent of mesh geometry. Once
the reactions have been simulated and mobile quantities updated within each cell, they
are transported.
Model application
This effort to study the effects of increasing model complexity was carried out as
part of a comprehensive testing process during the development of TaRSE. In addition
to the necessary quality control provided by sensitivity and uncertainty analyses, the
intention of this analysis was to study potential consequences resulting from the novel
freedom afforded by TaRSE’s flexible design (i.e., user-defined complexity). In order to
isolate the effects of complexity, an artificial domain was created in which the sources of
variability extrinsic to complexity could be controlled and excluded. A 1,000 × 200-m
generic flow domain (Figure 5-3) was created and discretized into 160 equal rectangular
triangles (cells). Flow was set from left to right so that the inflow boundary consisted of
cells 1, 41, 81, and 122, and the outflow boundary consisted of cells 40, 80, 120, and
160. A no-flow boundary was applied to the top and bottom (longer) edges of the
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domain. To exclude the effects of transient flow, steady-state velocity was established,
and the effect of heterogeneities were managed by assuming spatially homogeneous
conditions. A constant velocity of 500 m/d was established to approximate Everglades
flow conditions (Leonard et al., 2006) with an average water depth of 1.0 m.
Simulations were run for 30 days with a 3-hour time-step.
Levels of complexity
Three models of increasing complexity were created (Figure 5-4a-c). Following
the recommendations of Chwif et al. (2000), complexity was progressively added to the
model in an organized and step-wise fashion. Each new complexity level corresponded
to the addition of one new state variable and the associated processes relating the
variable to the pre-existing system. The simplest case (Level 1) contained no biotic
components (Figure 5-4a). The intermediate-complexity case (Level 2) contained
surface-water biota in the form phytoplankton (Figure 5-4b). The most complex case
(Level 3) contained additional macrophytes rooted in the soil (Figure 5-4c). Table 2-1
lists the state variables and processes that appeared in each complexity level, including
the boundary conditions for the mobile state variables (always quantified in g/m3), viz.
soluble reactive phosphorus (SRP) in the surface-water (CswP) and plankton biomass
(Cpl). Initial conditions for the stabile state variables (always quantified in g/m2), viz.
SRP in the porewater, adsorbed phosphorus, macrophyte biomass, and organic soil
mass, were 0.05, 0.027, 500, and 30,000 g/m2, respectively. Boundary and initial
conditions were selected to represent reasonable Everglades conditions based on
values cited in the extensive literature review conducted as part of parameterization
effort required for the sensitivity analyses (see following section). For full details of the
model equations and numerical solutions see Jawitz et al. (2008).
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Parameterization of Inputs Across Complexity Levels
The application of TaRSE was done without prior calibration in order to avoid
limiting the potential range of physical conditions the model might be applied to, and
through which the effects of new complexity would be expressed. This also facilitated
testing of the model across a wide range of possible scenarios as a necessary step in
the development process prior to evaluation of its performance for a particular
application (Saltelli et al., 2000). Results from the GSA and UA were evaluated to
ensure that simulation results were consistent with the conceptual models and that
unreasonable results did not emerge (see Jawitz et al., 2008 for extensive details).
Before conducting a GSA or UA it is necessary to specify a range and distribution for
each parameter, from which values can be statistically sampled.
The field-scale ambient variability of many inputs has been reported to be
adequately modeled with log-normal or Gaussian distributions (Jury et al. 1991; Haan et
al. 1998; Limpert et al. 2001; Loáiciga et al. 2006). When there is a lack of data to
estimate the mean and standard deviation for such PDFs, the (beta) β-distribution can
be used as an acceptable approximation (Wyss and Jørgensen 1998). When only the
range and a base (effective) value are known, a simple triangular distribution can be
used (Kotz and van Dorp 2004). Finally, a uniform distribution is recommended in
cases where values are assumed equally distributed along the entire parametric range.
The input parameters used in the analysis of TaRSE (Table 5-2) were assigned
ranges and probability distributions based on an extensive literature review found in
Jawitz et al. (2008). Since the goal of this work was a general model investigation, and
not a specific study of its application to a particular site, parameter ranges were
selected to cover all physically realistic values for the intended target region (the
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Everglades). Given the wide range of physical and ecological conditions that the data
from such an all-encompassing approach include, and considering that values were
derived from relevant literature rather than directly from sets of data, the more general
β-distribution was adopted. Consequently, all biogeochemical parameters (i.e.,
excluding transverse and longitudinal dispersivity) were described using β-distributions.
Dispersivity is related to the composition of the physical system, such as for example
vegetation density, domain dimensions, and velocity. These characteristics are
contingent on the site selection, rather than natural variation, and their probability was
therefore considered to be random, and accordingly allocated a uniform distribution
(Jawitz et al., 2008).
Several outputs were defined for the analysis, accounting for each of the model’s
state variables at each complexity level, and described in Table 5-1. In the context of
this work to investigate the role of complexity, only those outputs that appear in all three
complexity levels permit comparison and are presented. Outputs were defined to
integrate both spatial and temporal effects. For outputs of mobile quantities, averages
across the outflow domain (cells 40, 80, 120, and 160) were calculated at the end of the
simulation period in order to integrate the effects of transport parameters and processes
across the entire domain into the output. For stabile quantities, outputs were expressed
as the difference between the initial and final value of averages across the entire
domain.
Given the constancy of conditions applied to the model across all complexity levels
through fixed parameter ranges and distributions; invariant scale, initial, and boundary
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conditions; and steady hydrodynamics, any changes observed in the uncertainty and
sensitivity are attributed to the effects of changes in model complexity.
Results and Discussion
Effects of Model Complexity on Sensitivity
Morris method
Figures 5-5a-c depict trends in the results from the Morris method analysis for
soluble reactive phosphorus (SRP) in the surface-water, CswP. This output is generally
considered to be of greatest interest in management of water-quality for CERP (Perry,
2008), and is the official water-quality restoration target mandated by Congress (Sheikh
and Carter, 2005). Immediately apparent is that the relative location of parameters in
the µ*-σ plane changed as the complexity increased. At lower complexities (Levels 1
and 2) inputs were found closer to the µ*-axis, almost never approaching, and never
exceeding, the 1:1 line. At Level 3 the parameters were generally above the 1:1
(shaded triangle in each graph) and associated with proportionally larger σ-values.
Higher σ-values denote a greater role for interactions among input parameters. As the
complexity increased, more parameters were drawn out into the µ*-σ plane, particularly
at Level 3. Since important parameters (i.e., those to which C swP is most sensitive) are
distinguished from unimportant ones by their relative distance from the origin, these
results indicate that more parameters became relatively important as complexity
increased. Conversely, fewer parameters were uniquely important in the more complex
model. This trend is generalized in Figure 5-5d, a novel presentation of Morris method
results that takes advantage of the geometry inherent to their interpretation. Multiple
outputs were plotted collectively (CswP, CpwP, So, and SP) by normalizing the points to
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conserve their relative Cartesian positions, and grouping them by complexity level for
comparison. The same patterns observed in the C swP results are exhibited by all the
outputs lumped together in this way.
These results are in agreement with our hypothesis that as complexity increases,
an increase in interactions is associated with a decrease in direct effects. The
sensitivity of CswP to different parameters at different complexities shows the changing
role of certain parameters as others are added. In Level 1, the stabile parameters kox,
kdf, ρb and Xso (oxidation rate, coefficient of diffusion, soil bulk density, and the soil
phosphorus mass fraction, respectively) were the most important. In Level 2, plankton
in the water column was added to the model, and parameters associated with plankton
growth (kgpl and k1/2pl; plankton growth rate and plankton phosphorus half-saturation
constant, respectively) became the most important to CswP. With the addition of
macrophytes in Level 3, it became difficult to separate obviously important parameters.
Instead, the model became comparably sensitive to many parameters because of the
increased role of interactions.
Extended FAST
Quantitative results for CswP from the extended FAST analysis (Figs. 5-6a-h)
corroborate the qualitative Morris method results. The percentage of total variance
(Figure 5-6a) attributable to direct (first-order) effects (Si) decreased with increasing
complexity, slowly from Level 1 to 2, then rapidly from Level 2 to 3. The same trends
were exhibited by CpwP, So, SP (Figure 5-6b-d). Conversely, interaction effects (Figure
5-6a-d) rose slowly from Level 1 to 2, then rapidly from Level 2 to 3. These trends were
consistent across all model outputs and provide further quantitative evidence in support
155
of the hypothesized sensitivity-complexity relationship, as posited by Snowling and
Kramer (2001) and extended globally herein.
In Level 1, the sensitivity of C swP to parameters associated with stabile state
variables was limited by the coefficient of diffusion (see Figure 5-3a), because diffusion
was the physical link between mobile surface-water and stabile subsurface state
variables. In Level 2, the total sensitivity (Figure 5-6e) of CswP increased because the
addition of plankton introduced a number of parameters that could affect CswP without
first being channeled through, and thus dampened by, the slow process of diffusion. By
contrast, the Level 2 sensitivity of stabile outputs (CpwP, S o and SP) to parameters more
closely associated with either of the mobile state variables (CswP or C pl) remained
mitigated by the diffusion rate (Fig 5-6f-h). This changed in Level 3, however, where the
addition of macrophytes introduced new parameters to the subsurface. At this level of
complexity, macrophytes represented a phosphorus-sink dominant enough to make all
outputs sensitive to even those parameters whose influence was dampened by the slow
rate of diffusion. Consequently, we see a consistent trend across all outputs of
decreasing direct effects, and increasing interactions and total sensitivity. These results
indicate that the system was more sensitive to the addition of macrophytes than to
plankton. Furthermore, when viewed in conjunction with our understanding of the
physical description of the system, they allow us to understand how the model’s internal
dynamics, expressed as output sensitivities, are shifting with increasing complexity.
Effects of Model Complexity on Uncertainty
Some of the uncertainty results (Figs. 5-6e-h), presented here using the 95%
confidence interval, seem to question the conceptual trends in Hanna (1988) (Figure 51a), indicating that these relationships may not be as simple as proposed. In fact, this is
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explainable by accounting for the fact that some outputs are integrative, in that all
system components can participate in producing their final outcome, whereas others
have inherent biases that inhibit such integration. The key output, CswP, is an example
of an integrative output, since it is subject to the influence of all other state variables,
and the expected reduction of uncertainty holds. By comparison, accreted organic soil
(So), which is defined in terms of mass that is several orders of magnitude larger than
any other outputs, is not subject to comparable influence by other model components,
and is therefore not integrative. Mechanistically, this discrepancy is due to the relative
influence of turnover rates for the component compared with the fluxes into and out of
the store.
The consistent increase in uncertainty exhibited by So (Figure 5-6f) therefore does
not follow the conceptual trend. Interestingly, in Level 2 we saw that the stabile outputs
closely associated with So (C pwP and SP, which we might expect to be more integrated),
followed the S o trend and became more uncertain. This corresponds well with the
physics of the model for that level, however; addition of phosphorus through oxidation is
the predominant contributor to CpwP, to which SP is in turn bound through equilibrium
adsorption-desorption kinetics. Thus, their uncertainties should in fact be coupled with
that of So. This demonstrates that the uncertainty effects in poorly integrated outputs
can be passed onto related outputs, effectively dis-integrating them. With the
introduction of macrophytes in Level 3, the effect of So on CpwP and S P was broken by
the addition of a major new sink for phosphorus released through oxidation of the
organic soil, the process that physically linked the three outputs. The previously
affected outputs in turn became more integrated, and we see their uncertainty drop as
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originally expected (Figure 5-6h). It is therefore important to consider that outputs can
be effectively dis-integrated, and therefore may not receive the consequences of
increasing complexity in the same way. Similarly, outputs may not be affected by added
complexity in other parts of the model.
Figures 5-7a-c depict the progression of output PDFs across complexity levels for
the same key output, CswP, from a simpler leptokurtic distribution at the lowest
complexity level (represented by the lowest number of input parameters, eight), through
the platykurtic distribution at the intermediate level (12 parameters), to a bimodal
distribution at the highest complexity (16 parameters). The latter results represent
different system states, combining the further platykurtic nature of the Level 2 stablestate, with a strongly leptokurtic end-point that corresponds to combinations of
parameter values that push the simulation out of the original stable-state. In this case,
the alternate state appears as a single value, and indicates that the complexity at this
level was sufficient to capture the existence of a second state, but insufficient to capture
any variability within the state.
Mechanistically, the presence of this second state demonstrates that a critical
threshold existed for the state previously simulated as Level 2. Its presence was
caused by combinations of parameter values working in conjunction with initial and
boundary conditions, which resulted in the systemic depletion of the biotic components
(plankton and macrophytes). This occurred because the range of values over which the
parameters were varied was held constant across complexity levels, yet included values
appropriate for both of the known stable-states that shallow water bodies can exhibit in
the Everglades (Scheffer, 1990; Scheffer et al. 1993; Beisner et al., 2003;), namely
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algae- and macrophyte-dominated systems (Bays et al. 2001; Cichra et al. 1995).
Testing the full range of plankton-dominated conditions in Level 2 presented no
problems to the model because the structure was mechanistically appropriate – there
were no macrophytes. However, the incorporation of macrophytes into the model
structure changed the definition of the simulated ecosystem, and without the necessary
feedback mechanisms (i.e., complexity) in place to resolve the extreme conditions
produced by unrealistic combinations of parameter values, phytoplankton biomass is all
but eliminated. Without this surface-water sink for phosphorus, CswP continuously input
at the boundary remained essentially unchanged in these cases, depicted by the spike
in outflow values matching the boundary concentration of 0.05 g/m3 (Figure 5-7c) The
platykurtic area represents model conditions under which the simulated system is not
catastrophically overwhelmed. The results therefore mimic those of Level 2, where
macrophytes were absent and phytoplankton dominated the surface-water phosphorus
dynamics. It is noteworthy that the introduction of macrophytes still acts as a
phosphorus sink in these cases, stressing the phytoplankton in terms of phosphorus
availability and thereby dampening the frequency of lower CswP values (a sign of greater
phosphorus uptake due to growing plankton). Macrophytes also prevent the majority of
CswP results from exceeding the boundary input concentration (which can only occur
when significant diffusion takes place due to high CpwP, as in Level 2, and as was never
the case for Level 3 because of porewater SRP uptake by the macrophytes (Jawitz et
al. 2008).
In this way, the addition of macrophytes to the set of tested model conditions
represented the introduction of an alternate stable-state that could not be resolved. The
159
complexity was insufficient to permit the model to simulate a shift between stable-states,
but (in conjunction with the parameter ranges tested for) was sufficient to simulate the
existence of a second stable-state. Though these results express emergent
characteristics of the simulated systems under the tested conditions, the forcing
“functions” in this case (being the variously sampled parameter sets) are based on real
values (albeit not necessarily real combinations of values) and therefore represent
potential realities that match well with the known biotic states of the Everglades: mixed
algae-macrophyte (the hump in Figure 5-7c) and macrophyte-dominated (the spike).
Given the absence of any suitable feedback in the tested model’s mechanisms that
might permit plankton to dominate macrophytes, such a stable state is impossible to
simulate. The emergence of alternate stable-states in the results only occurs once
complexity has reached Level 3, clearly indicating that additional model complexity is
required to capture the complicated, but real, behavior of the system.
Conclusions
Presented results have corroborated the sensitivity-complexity relationship,
proposed by Snowling and Kramer (2001), using true global sensitivity methods and
over a wide range of model conditions, thereby demonstrating the validity of the
relationship in the most general context yet. We have also demonstrated that our
hypotheses relating the global sensitivity indices for direct effects, interactions, and total
sensitivity to model complexity are valid, providing a fresh global perspective to the
relevance trilemma.
The combined GSA and UA framework applied herein produced valuable insights
for interpreting both the meaning of the model results, and the meaning of how they
were generated in the context of model relevance. This methodology is therefore
160
proposed as a useful way to glean insights into the external and internal dimensions of
model performance.
The combined GSA and UA results presented indicate that uncertainty, on
average, decreases with complexity, and that total sensitivity increases. This implies
that we are still within the region of the trilemma space (Figure 5-2) that encourages us
to persist with increasing complexity if so desired. These results emerged from an
exploration of parametric spaces far larger than would be expected for any application
to a specific site, and therefore constitute a worst-case-scenario, which is thus cause for
further optimism. It is therefore reasonable to expect that refinement to a particular
application will reduce uncertainty further and permit additional complexity without loss
of relevance.
Given the benefits derived from the GSA/UA methods, it is proposed that these
methods constitute a valuable framework (Figure 5-8) for exploring the Relevance
Trilemma. In applying it herein, we gained useful information about the tested versions
of TaRSE, including important considerations valuable to future work, such as the
sensitivity of outputs to particular parameters, the strong effects caused by introducing
macrophytes, and the importance of considering integration in output definitions. The
sensitivity of the model to the addition of macrophytes calls for close attention to the
associated initial conditions and parametric ranges. The emergence of alternate stable
states in Level 3 results, and their absence in simpler levels, demonstrates the need for
some minimal complexity if such real world patterns are to be reproduced in
simulations, and highlights the unexpected potential for such patterns in the output
response of even a relatively coarse biogeochemical model. Importantly, these
161
methods also provide insights into how one might reduce model uncertainty (Saltelli et
al., 2004) by identifying important and unimportant parameters and processes. This
information can be used to guide efforts to better measure important parameters or
remove ineffectual complexity.
Important questions remain after the analyses presented here. Does Level 3
represent the optimum system description? Can this optimum be determined?
Although answers to these questions fall, at least in part, into the subjective realm of the
"art of modeling," the tools presented here offer the modeler an opportunity to better
understand the sometimes unexpected tradeoffs introduced by increasing model
complexity. We suggest that today we are in a better position to unravel the relevance
trilemma, and indeed even to actively incorporate it into our art, than when Zadeh
(1973) first presented his principle of incompatibility.
162
Table 5-1. Process description for the increasing levels of complexity studied
Process
Levels
Key, fig5-2
Affected variables
Process equation
Surface-water SRP concentration (mobile),
P
3
Csw (g/m )
Diffusion
Sorption-desorption
Oxidation of organic soil
Inflow/outflow of surfacewater SRP
Uptake of SRP through
plankton growth
Settling of plankton
Inflow/outflow of
suspended particulates
(plankton)
Uptake of porewater SRP
through macrophyte
growth
Senescence and
deposition of
macrophytes
1, 2, 3
1
Soil porewater SRP concentration (stabile),
P
2
Cpw (g/m )
Soil porewater SRP concentration (stabile),
P
2
Cpw (g/m )
1, 2, 3
2
1, 2, 3
3
1, 2, 3
4
Soil adsorbed P mass (stabile), S (g/m )
P
dS P ρ b k d dC pw
=
dt
dt
θ
Soil porewater SRP concentration (stabile),
P
2
Cpw (g/m )
Organic soil mass (stabile), So (g/m2)
dS o
= −k ox S o
dt
Surface-water SRP concentration (mobile),
P
3
Csw (g/m )
BC: CswP = 0.05 g/m3
P
2
Surface-water SRP concentration (mobile),
CswP (g/m3)
pl
2, 3
5
Plankton biomass concentration (mobile), C
3
(g/m )
Plankton biomass concentration (mobile), Cpl
(g/m3)
2, 3
2, 3
6
7
Organic soil mass (stabile), So (g/m2)
Plankton biomass concentration (mobile), Cpl
3
(g/m )
Soil porewater SRP concentration (stabile),
P
2
Cpw (g/m )
3
8
Macrophyte biomass (stabile), Cmp (g/m2)
mp
(g/m2)
Macrophyte biomass (stabile), C
3
9
(
P
dC sw
k
P
P
= df C pw
− C sw
dt
zw zdf
o
2
Organic soil mass (stabile), S (g/m )
163
)
 CP

dC pl
= −k gpl C pl  P sw pl 
dt
 C sw + k 1/ 2 
pl
dC sw
= −k stpl C pl
dt
BC: Cpl = 0.043 g/m3
P


C pw
dC mp

= −k gmpC mp  P
 C + z θk mp 
dt
as
1/ 2 
 pw
dC mp
= −k snC mp
dt
Table 5-2. Probability distributions of model input factors used in the global sensitivity
and uncertainty analysis
Parameter
definition
Symbol
Process in
Fig5-4
Distribution
Units
Input present
in
L1 L2 L3
Coefficient of
diffusion
kdf
1
β (7×10-10, 4×10-9)
m2/s
x
x
x
Coefficient of
adsorption
kd
2
β (8×10-6, 11×10-6)
m3/g
x
x
x
Soil porosity
θ
2
β (.7, 0.98)
-
x
x
x
Soil bulk density
ρb
2
β (.05, 0.5)
-
x
x
x
Soil oxidation rate
kox
3
β (.0001, 0.0015)
1/d
x
x
x
P mass fraction in
organic soil
ΧsoP
3
β (.0006, 0.0025)
-
x
x
x
Longitudinal
dispersivity
λl
4
U (70, 270)
m
x
x
x
Transverse
dispersivity
λt
4
U (70, 270)
m
x
x
x
Plankton growth
rate
kgpl
5
β (.2, 2.5)
1/d
x
x
Plankton half
saturation
constant
k1/2pl
5
β (.005, 0.08)
g/m3
x
x
Plankton settling
rate
kstpl
6
β (2.3×10-7, 5.8×10-6)
m/s
x
x
P mass fraction in
plankton
ΧplP
6
β (.0008, 0.015)
-
x
x
Macrophyte
growth rate
kgmp
8
β (.004, 0.17)
1/d
x
Macrophyte half
saturation
constant
k1/2mp
8
β (.001, 0.01)
g/m3
x
Macrophyte
senescence rate
ksnmp
9
β (.001, 0.05)
1/d
x
P mass fraction in
macrophytes
ΧmpP
9
β (.0002, 0.005)
-
x
164
Figure 5-1. Relevance relative to a) sources of modeling uncertainty in relation to
model complexity (Hanna, 1988 as cited in Fisher et al., 2002), and b)
Snowling and Kramer’s (2001) hypothesis relating error and sensitivity to
model complexity.
165
Figure 5-2. Hypothesized trends relating complexity to sensitivity from direct effects,
sensitivity from interactions, and total sensitivity. Total uncertainty still follows
the trends of Hanna (1988) but now includes total sensitivity as another
source of uncertainty.
Figure 5-3. TaRSE application domain, with flow from left to right and bounded above
and below by no-flow boundaries. Simulations were run for 30 days with a
time-step of 3 hours.
166
Figure 5-4. Levels of modeling complexity studied to represent phosphorus dynamics in
wetlands. Levels include a) Level 1: interactions between SRP in the water
column and SRP in the subsurface; b) Level 2: Level 1 with the addition of
plankton growth and settling; c) Level 3: Level 2 with the addition of
macrophyte growth and senescence. Notation and details on processes
included in each Level are given in Table 2-1.
167
Figure 5-5. Morris method global sensitivity analysis results for surface-water soluble
reactive phosphorus outflow (C swP) in a) Level 1, b) Level 2, c) Level 3, and
for d) all outputs and all levels combined. The grey triangles indicate the 1:1
line, font size of labeled parameters indicates their relative importance to
CswP.
168
Figure 5-6. Results for a-d) sensitivity from direct effects (Si, left y-axis) and sensitivity
from interactions (ST - Si, right y-axis, and e-h) output uncertainty expressed
as the 95% CI (left y-axis) and total sensitivity (S T, right y-axis), as model
complexity was increased.
169
Figure 5-7. Output PDFs for SRP concentration in surface-water outflow (CswP) for a)
Level 1, b) Level 2 and c) Level 3.
170
Figure 5-8. A suggested framework, employing global sensitivity and uncertainty analyses, for enhancing understanding
of model performance studying model relevance in relation to complexity
171
CHAPTER 6
CONCLUDING REMARKS
Conclusions
A novel water-quality modeling tool has been developed for the coastal wetlands
of the southern Everglades by linking the hydrologic model FTLOADDS with the waterquality model aRSE to create FTaRSELOADDS. FTaRSELOADDS combines the
numerical efficiency and mechanistic rigor of a fixed-form spatially-distributed
hydrodynamic model with the adaptability of a flexible free-form biogeochemical cycling
model. In combination, the two models represent a tool that can be adapted and refined
to best capture the water-quality issue of interest while accounting for the complex
variable-density unsteady hydrodynamics that characterize the region’s hydrology The
linkage of the FTLOADDS and aRSE was validated by a series of comparisons between
known analytical solutions and numerically simulated results that used FTLOADDS and
a combination of FTLOADDS and aRSE. Thus Objective 1 was satisfied.
The linked models were tested with a field application to the SICS region, which
provided answers to the questions underlying Objectives 2 and 3. Surface-water
hydrodynamics were shown to be sensitive to depth-varying Manning’s n, which had to
be reintroduced into the hydrodynamic model in order to accurately capture wetting and
drying processes and their effects on water-quality. Three different water-quality
conceptual models of increasing complexity were implemented and the results
compared. The simplest version employed conservative transport and produced the
best match with data. However, this version also neglected all biogeochemical
processes, including the important input of atmospheric deposition, and was therefore
the weakest of the models from the perspective of mechanistic justifiability. The most
172
complex model produced acceptable results despite being subject to the significant
uncertainty associated with including atmospheric deposition, implying that the greater
mechanistic integrity may have helped mitigate this uncertainty. Experimentation with
how to input atmospheric deposition indicated that the simplest approach of distributing
an annual average equally over all days in the course of a year produced the best
results and is justifiable based on the limited data available.
Given the freedom to manipulate model complexity, and the recognized
relationship between this complexity and model uncertainty, sensitivity and relevance, a
study was conducted to elucidate how additional complexity affects model performance
(Objective 4). Global sensitivity and uncertainty analysis methods were applied, and a
framework for formally exploring their results in the context of complexity was
presented. Direct sensitivity was found to decrease and interaction effects to increase
as complexity was added. Uncertainty was found to decrease in response to increased
complexity, though considerations of turnover rates versus flux rates were shown to
influence this result. The suggested framework demonstrated its value as a useful
means of exploring and explaining model results and of assessing relevance with
respect to complexity, thus satisfying Objective 4.
Limitations
Currently, the computational expense of a fully integrated fixed-form/free-form tool
remains high. The required time-step for hydrodynamic simulations of SICS is small but
the efficiency of solution methods keeps the investment manageable. With the addition
of aRSE comes significant overhead since each cell in the SICS hydrodynamic model
domain is individually processed. This process is exacerbated by the need to prepare
and exchange large amounts of data between the two models. The presented effort
173
was limited to a daily time-step by these computational costs, which precluded using the
Runge-Kutte 4th Order differential equation solution functionality within aRSE, which
required a maximum 15-minute time-step and untenable cumulative computational
times.
The paucity of surface-water phosphorus data was a significant limitation to the
water-quality modeling effort. This was exacerbated by the fact that observed
phosphorus concentrations fluctuated within a relatively small range of variation due to
the oligotrophic conditions. A more rigorous testing of the water-quality against more
phosphorus concentration data points, or against more types of data (such as
biomasses or fluxes), would contribute valuable additional validation of the model.
Additionally, the sensitivity and uncertainty analyses performed did not evaluate
the SICS water-quality application, but rather a theoretical application established in a
generic testing domain. The SICS water-quality application would benefit from such a
sensitivity and uncertainty analysis. Similarly, evaluation the complexity-relevance
relationship for a field-tested application such as SICS would provide additional rigor to
the testing of the suggested relevance framework.
Finally, there is currently no formal documentation for aRSE or FTaRSELOADDS.
Documentation does exist for TaRSE and SWIFT2D individually, but a formal record of
the linkage of the models and a user’s manual to guide implementation of the linked
tools is needed. Without this documentation the complexity of the tool prevents its
wider application by any user not already familiar with it.
Future Research
Future work is required to either extend the simulation period to include more data
points, or to shift the simulation period to more recent times when data is being
174
recorded at greater resolution. Additional time-series data pertaining to soil
phosphorus, periphyton and macrophyte biomass in the SICS region would provide
valuable additional testing of the more mechanistic water-quality modeling approaches.
The current treatment of the water-quality reactions as a completely separate step to
the transport means that parallelization of the reactions is possible. Considering that
over 9,000 cells are currently processed in linear sequential order when they could all
theoretically be processed simultaneously, the opportunities for greater computational
efficiency are significant.
The work presented here has demonstrated the significant commitment required to
get to the point of being able to make use of this tool. Future work must now explore
and expose the potential within, especially as it pertains to the flexibility provided by
aRSE. Most immediately, the mechanistic and spatially-distributed modeling of any
number of water-quality issues in the southern Everglades can begin in earnest.
Nitrogen and dissolved organic carbon input to Florida Bay are a major concern that has
not been satisfactorily addressed. The proven ability of the hydrodynamic model to
accurately capture wetting and drying is encouraging for future sulfur and mercury
modeling in the region given the importance of these processes to mercury methylation
(Cleckner et al., 1999).
The development of ecohydrological water-quality modeling is now also possible.
The important role of Manning’s n in the hydrological simulations was demonstrated in
Chapter 3. Making the link between simulating biomass growth for water-quality and
changes in flow resistance with seasonal growth and senescence is readily achievable
175
with FTaRSELOADDS. So too is the integration of spatially-distributed nutrient inputs to
ecological models in the region, which have previously been limited to hydrologic inputs.
Finally, such flexibility within complex models is an important launching point for
serious study of how model complexity, uncertainty, and sensitivity interact in complex
spatially-distributed models. Given the paucity of work in this field and the clear benefits
derived from the GSA and UA methodology that was applied in Chapter 5, the
framework that was proposed for tackling questions related to the Relevance Trilemma
should prove fruitful.
Philosophical Deliberations
The freedom to be creative is the source of progress. It is this tenet that underlies
the very notion of Academia, and recognizes the profound role of creative freedom in
advancing our technological, cultural, and intellectual evolution. It is the freedom to be
creative that will prove to be the greatest strength of tools such as FTaRSELOADDS.
One need look no further than the kaleidoscope of problems to which STELLA has
been applied to see the imagination unleashed by a tool that puts creative control in the
user’s hands. There is no reason why users of complex models, such as that applied
herein, should be denied such creative freedoms as a matter of course, as has long
been the case with the availability of only fixed-form spatially-distributed models. In
fact, it is precisely because modeling of this highly complex sort is so arduous, and so
challenging, that such freedoms should be encouraged. To have modelers who have
invested such energy and expertise and life time into mastering a tool that is subject to
claustrophobic specificity is to waste a glut of potential and opportunity.
The art of modeling will always entail balancing the pros and cons behind the
choice of an appropriate tool for a given problem, whether it be developed from scratch
176
or picked off a shelf. With the freedom to uniquely tailor complex spatially distributed
models comes a new dimension to the art modeling: the notion of optimizing these high
levels of complexity with respect to uncertainty, sensitivity and relevance. It is important
that we continue to delve more deeply into this tripartite conundrum or risk falling behind
our tools. Modelers, and all who depend on their work, cannot fail to acknowledge and
grasp the limitations to relevance inherent to the nascent generation of “super-complex”
tools, including efforts to integrate many independent and spatially-distributed models
into vast multi-model systems.
As complex model creation and modeler creativity become ever more entangled,
better understanding of how models gain and lose relevance is critical both to the
evolution of our tools and to the evolution of our modelers. We cannot forget that the
science and art of modeling are one and the same.
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APPENDIX A
MODEL VERSIONS
Model and Application Versions: Nomenclature
The following rules and naming conventions apply when referring to versions of
either SWIFT2D, FTLOADDS, or their applications as SICS or TIME:
SWIFT2D: specifies only the surface-water model
SEAWAT: specifies only the ground-water model
FTLOADDS: specifies versions in which SWIFT2D and SEAWAT have been linked (one
or the other may be on or off)
SICS: the Southern Inland and Coastal Systems application
TIME: the Tides and Inflows in the Mangroves of the Everglades application
Version 1.X: models or applications simulating only surface-water
Version 2.x: models or applications simulating coupled surface-water/ground-water
Version X.1: models or applications using SWIFT2D code adapted for the SICS
application as per Swain et al. (2004)
Version X.2: models or applications using SWIFT2D code adapted for the TIME
application as per Wang et al. (2007)
Version X.Y.1: models or applications using SWIFT2D code adapted for TIME but with
variable-Manning's functionality from SICS adaptations reinstated
Model and Application Versions: Sub-models
The following figures offer a graphical overview of the model and application
versions. Consistent colors are used to represent identical versions/models to facilitate
identification across figures. Perpendicular blocks, generally oriented vertically, indicate
models/versions that encompass adjacent horizontal blocks. Blocks crossed out in
white indicate that the submodel is present but not used.
178
Figure A-1. SWIFT2D v1.1 comprises the SWIFT2D v1.0 (Schaffranek, 2004) code and
additional code from SICS updates for coastal wetlands (Swain, 2005).
Figure A-2. FTLOADDS v1.1 comprises the SWIFT2D v1.1. code, leakage code linking
SWIFT2D to SEAWAT, and SEAWAT, but represents applications in which
SEAWAT is not implemented.
Figure A-3. SEAWAT comprises the MODFLOW code and the MT3DMS code
(Langevin and Guo, 2006).
179
Figure A-4. FTLOADDS v2.1 comprises SWIFT2D v2.1 and SEAWAT, where
SWIFT2D v2.1 is SWIFT2D v1.1 implemented with integrated leakage and
ground-water simulation by SEAWAT.
Figure A-5. FTLOADDS v1.2 comprises SWIFT2D v2.2 with updates for TIME but with
the ground-water simulation turned off (thus SWIFT2D v1.2).
180
Figure A-6. FTLOADDS v2.2 contains SWIFT2D v2.1 linked with SEAWAT and
containing TIME updates (thus SWIFT2D v2.2).
181
APPENDIX B
DETAILS OF THE FTARSELOADDS LINKAGE
Section B1
Technical Considerations in the Model Linkage
Since aRSE is callable as a DLL, and considering the primacy of hydrology and
the role of FTLOADDS in controlling the integrated execution of SWIFT2D and
SEAWAT, FTLOADDS was selected as the controlling program. Furthermore, the
decision was taken to link aRSE with the surface-water model only, i.e. to SWIFT2D.
This was done to keep the scope of the task manageable given the effort entailed in
linking aRSE to even one of the two complex FTLOADDS sub-models. The choice of
SWIFT2D is further justified by recognizing that the biogeochemical processes aRSE is
intended to simulate are primarily associated with the surface-water in wetlands
systems. Water-quality in the ground-water is generally not as sensitive to biological
influence given the paucity of autotrophic organisms and was therefore not justified at
this early stage development. Additionally, though vertical flow through the upper soil
cannot be simulated given these assumptions, the flexibility of aRSE does permit soil
phosphorus state-variables to be defined, which would permit soil biogeochemistry to be
modeled under assumptions of negligible vertical advection processes.
A number of fundamental differences in the respective design of FTLOADDS and
aRSE had to be overcome in order to successfully link the two models. These included
an idiosyncratic artifact of the initial setup of aRSE that inhibited its automation within
FTLOADDS, the absence of a spatial distribution in aRSE, and the use of different
programming languages to code the models.
182
Consideration 1: Initial setup of aRSE
In order for the user to specify a unique system of water-quality processes it is
necessary to input the state-variables that comprise the system, the parameters
required to characterize the equations relating the state-variables, and the nature of the
equations themselves. State-variables are classified as mobile if they represent
constituents that would be moved with flow (solutes and suspended particulates –
constituents), or stabile if they represent stationary quantities (e.g. rooted macrophytes,
soil, benthos). There are also 30 additional implicit parameters that are always present,
though only used if specified in the equations. These implicit parameters were originally
necessary for transport processes and have been kept because they represent useful
properties (mostly of hydrodynamics) that may be useful in future work and present little
inconvenience with their presence. In the jargon of aRSE, state-variables and
parameters are collectively referred to as components. Given that the number of both
parameters and state-variables is a user choice, the total number of components is
variable.
A single vector, VARS, is used by aRSE to store the values for all components. In
order for updated values of transported constituents or hydrodynamic quantities to be
passed from FTLOADDS to aRSE it is necessary to know which particular element of
this vector corresponds with the given quantity. However, aRSE must be initialized
once in order to determine these locations since they are subject to the number of userspecified components. In order to exchange information between the two models it is
necessary to have some means to determine what quantity each element of the vector
refers to.
183
Consideration 2: Spatially-distributed versus non-spatial
FTLOADDS is a spatially-distributed model, and therefore performs calculations
on, and stores data about, many individual cells that together comprise the modeled
domain. By contrast, aRSE is non-spatial, assuming that the system of reactions it
simulates is carried out at a singular location with no consideration of spatial
distribution.
Where FTLOADDS stores arrays of data for each model variable, aRSE stores a
single vector containing the single value for each of the model components. The use of
a one-dimensional vector, as opposed to a higher-dimensional array, is possible
because there is essentially only ever one cell (hence non-spatial) under consideration.
By contrast, SWIFT2D maintains two-dimensional arrays, dimensioned to the total
number of cells used to discretize the model domain, for each of the hydrodynamic
variables and three-dimensional arrays for the solute concentration variables (the third
dimension is used to specify the particular constituent, since all concentrations for up to
seven constituents are stored in a single array).
Since aRSE can only ever consider a single cell at a time it must be run repeatedly
for each of the cells in the FTLOADDS domain. This in turn entails updating the VARS
values with data appropriate to the cell in question, and then saving the values after the
reactions step so they are not over-written by the results of the subsequent cell’s
reaction step.
Consideration 3: FORTRAN versus C++
The programming languages used to encode each of the models was not
consistent. The FORTRAN language (in the form of both FORTRAN 77 and FORTRAN
90) was used to code FTLOADDS and its constituent sub-models, SWIFT2D and
184
SEAWAT. The generic design of aRSE is the product of object-oriented template
functionality in the C++ language used to code it. The linkage of the two models
therefore represents a mixed-language programming problem in which communication
between the two structurally and syntactically foreign languages must be facilitated.
A number of inter-language calling conventions have been adopted by FORTRAN
and C/C++ (Arnholm, 1997; Wang et al., 2005):
•
Most FORTRAN compilers convert subroutine names to lower case and append
an underscore. To make a C routine callable in FORTRAN, declare the name of
the routine in lower case and append an underscore.
•
FORTRAN passes arguments by reference, C++ by value. For a variable name
in a subroutine call from FORTRAN, the corresponding C routine receives a
pointer to that variable. When calling a FORTRAN routine, the C routine must
explicitly pass addresses (pointers) in the argument list.
•
C routines assume that character strings are delimited by the null character.
From FORTRAN to C, the length of each character string is passed as an implicit
additional INTEGER (KIND=4) value, following the explicit arguments. From C to
FORTRAN, when a function returns a character string, the address of the space
to receive the result is passed as the first implicit argument to the function, and
the length of the result space is passed as the second implicit argument,
preceding all explicit arguments.
•
Arrays in FORTRAN are stored in a column-major order, whereas in C they are
stored in a row-major order. Two types of communication between FORTRAN
and C++ were required that called for special treatment.
Wang et al. (2005) outline a suggested manual procedure for overcoming these
problems. The principle is to build a “wrapper” for the C++ library that hides the
implementation details of the library from the FORTRAN code. The wrapper handles
the request from a FORTRAN call to create and destroy the objects defined in C++, and
then returns a FORTRAN pointer aliased to the memory allocated in the C++ library with
support function overloading. The “wrapper” itself is made of two components, one “C”
and one FORTRAN 90 component, written in “standard” C++ and FORTRAN 90,
185
together with the conventional inter-language calling method. Changes to the
application source code are minimal and can be automated.
The FORTRAN 90 component contains a module that provides a set of public
functions for the FORTRAN application to call. Each of these public functions
corresponds to a function implemented in the C++ library, and it calls the corresponding
function via the C++ component. The FORTRAN 90 module also holds one- or multidimensional FORTRAN pointers in its global space, and thereby provides an alias
function for the C++ component to call that makes the one- or multi- dimensional
FORTRAN pointer aliased to the memory space allocated dynamically in the C++
library.
Resolution 1: Initial setup of aRSE
To overcome this problem a FORTRAN subroutine, READIWQ, was written to
read a new water-quality input file (IWQINPUT.iwq) that contains the necessary data
also included in the XML input file, but which could be read without the need for aRSE
to be executed. The XML output file was therefore no longer needed. Since aRSE still
relies on reading the XML input file to correctly setup, this method requires that two
input files containing some overlap in data be provided. However, the files are small
and simple to produce, and allow the setup of aRSE to be automated and controlled
from FTLOADDS. Furthermore, having such a file is also useful for overwriting aRSE
parameters and state-variable initial conditions should this be desirable, and introduces
some measure of control from within the calling FORTRAN code over the inputs to
aRSE without having to tamper with the aRSE code at all.
The automation process in READIWQ makes use of the fact that aRSE distributes
components in the VARS vector in an orderly manner that, given knowledge about the
186
number of state-variables and the number of parameters, permits the deduction of their
future location in VARS vector. Mobile state-variables are always positioned first,
followed by stabile state-variables, followed by a fixed number of implicit parameters (27
hydrodynamic and spatial properties), followed by the user-input parameters, followed
by the remaining 3 implicit parameters (temporal properties). The subroutine READIWQ
therefore requires, in order:
The number of mobile state-variables
The number of stabile state-variables
The paired name and initial value for each mobile state-variable
The paired name and initial value for each stabile state-variable
The number of user-specified parameters
The paired name and value for each user-specified parameters
Also permitted are override values for any of the implicit parameters, whose positions in
VARS are fixed relative to each other, though contingent in absolute position on the
number of state-variables that precede them. This process is conducted during the
initial setup of SWIFT2D, thereby ensuring that data is correctly exchange and the
linkage with aRSE is fully functional from the first time it is called from within SWIFT2D
(though aRSE still requires its own initialization step the first time it is called to process
the equations outlined in the XML input).
Resolution 2: Spatially-distributed versus non-spatial
A new two-dimensional vector was established, C1_aRSE, dimensioned to the
number of components (i.e. the same size as the VARS vector) and the total number of
cells in the FTLOADDS domain. Each time aRSE is called, which may or may not be
coincident with the FTLOADDS hydrology and transport time-steps, all the appropriate
data for each of the cells is moved from the various arrays within FTLOADDS to
C1_aRSE prior to the simulation of reactions in the first cell. Since no exchange of
187
information between cells takes place during the reaction step, the order in which cells
are processed for reactions does not matter with regards to the accuracy of the
simulation. However, the order in which memory is accessed during computations does
affect the speed of the process. It date are therefore transmitted in column-major order
from FTLOADDS arrays to C1_aRSE in order to minimize computational time. Though
FTLOADDS arrays are dimensioned with a rectangular shape (number of rows x
number of columns), the model permits an irregularly shaped domain, which may result
in many points within the rectangular memory array referring to cells that are not
actually used by FTLOADDS. The subroutine CELLCOUNT therefore determines the
number of active cells in the model and this number is used in the reactions step,
thereby minimizing the computational iterations
Prior to each individual cell being processed the data appropriate to that cell is
transmitted to the VARS vector that is used directly by aRSE. Once the reactions have
been simulated the updated VARS values are used to overwrite old values in C1_aRSE.
In this way old values are overwritten and new values stored until reactions have been
performed on all cells. After the final cell has been processed, all updated values in
C1_aRSE used transmitted back to their appropriate FTLOADDS arrays, where they
are then used in subsequent transport calculations.
Currently, concentrations, depths, and velocity in the x- and y-directions are
passed from FTLOADDS to aRSE, where concentrations are analogous to mobile statevariables, and the hydrodynamic variables to particular implicit parameters. Only
concentrations are transmitted back to FTLOADDS for use in transport, though the
freedom to return updated hydrodynamic variables should the reactions affect them
188
offers potentially exciting opportunities for simulating ecohydrological effects using
these models.
Resolution 3: FORTRAN versus C++
Text strings in FORTRAN and C++ are represented differently. FORTRAN strings
are character variables that are declared as a particular length, which is maintained by
trailing blank space characters irrespective of the length of the text of interest within the
string. By contrast, C++ strings are null-terminated following the final character of text.
If FORTRAN strings are to be understood by C++ they must be converted to a nullterminated form. A subroutine to do so exists, and was used to convert the XML input
filenames, which are now read in by the FORTRAN subroutine READIWQ, and convert
them to a format acceptable to the C++ code of aRSE.
The second instance necessitating mixed-language communication was the calling
of subroutines. In this case, aRSE is executed by calling one of a three C++
subroutines from within the FORTRAN linkage. FORTRAN 90 contains some built-in
functionality to facilitate mixed-language programming, including the INTERFACE
statement, which is useful for creating interfaces between FORTRAN and external
subroutines. Interfaces were therefore defined for each of the external C++
subroutines. Compiler directives were specified within the interface to attribute C++
calling conventions, to specify the location of the subroutines as within a DLL, and to
specify an alias for the called subroutine that was preceded with an underscore to
match the C++ syntax.
General description of the linkage mechanism
•
If aRSE is greater than zero then READIWQ is called during the setup of SWIFT2D
to preprocess aRSE.
189
•
The subroutine CALLaRSE is called at the time interval specified by the variable
CaRSE.
•
Prior to performing reactions on the first cell the subroutine aRSE_IN is called to
transfer the values for all specified FTLOADDS variables in each of the domain cells
to the storage array variable C1_aRSE.
•
For each cell in turn the subroutine RUN_aRSE is called, which updates the vector
VARS with the cell-specific values and calls the C++ subroutines PRESOVE,
RKSOLVE and POSTSOLVE to execute aRSE. If it is the first time aRSE is being
called then the subroutine INITIALIZE is called prior to these subroutines. After each
cell has been processed the array variable C1_aRSE is updated with the updated
values in the vector VARS.
•
After reactions have been performed on the final cell the subroutine aRSE_OUT is
called to update all appropriate FTLOADDS variables with the new values in the
array variable C1_aRSE.
Section B2
FORTRAN Subroutines for Linkage
The following subroutines were written specifically for the linkage of aRSE and
FTLOADDS. Additional code that was added to existing SWIFT2D subroutines is given
in Section B3.
Module aRSEDIM
MODULE aRSEDIM
!****************************************************************************
*
! This MODULE is used for declaring variables used in the linkage of aRSE
! with SWIFT2D within FTLOADDS
!****************************************************************************
*
IMPLICIT NONE
INTEGER*4 INITIATE, NCALLS, NCELLS, NCELLST, NCOMPS, NCOMPST, NVARS
INTEGER*4 CALLNO, CELLNO, RKORDER, NPAR, NMOB, NSTAB, NSTABMAX, K_WET,
ATM_NPAR
PARAMETER (NCALLS = 1, NCELLST = 10201, NCOMPST = 60, RKORDER = 4,
NSTABMAX = 15)
INTEGER*1 XMLINPUTC(50), XMLOUTPUTC(50), XMLREAC_SETC(50)
INTEGER NPRZ(NSTABMAX)
CHARACTER*120 PREPROCESS, XMLINPUT, XMLOUTPUT, XMLREAC_SET,
COMPNAME(NCOMPST)
REAL*8 DTaRSE,DTFTLOADDS
190
!****************************************************************************
****
REAL*8, DIMENSION (:), PUBLIC, ALLOCATABLE :: ZR(:,:,:),
C1_aRSE(:,:),ZRIC(:,:,:),RIC(:,:,:)
PUBLIC :: SUB
CONTAINS
SUBROUTINE SUB (en,em,el,ze,comps,activecells)
!integer, intent(in) :: en,em,te
INTEGER :: en,em,el,ze,err,comps,activecells
ALLOCATE ( ZR(en,em,ze), stat=err)
ZR=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
ALLOCATE ( C1_aRSE(comps,activecells), stat=err)
C1_aRSE=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
ALLOCATE ( ZRIC(en,em,ze), stat=err)
ZRIC=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
ALLOCATE ( RIC(en,em,el), stat=err)
RIC=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
END SUBROUTINE SUB
END MODULE aRSEDIM
Subroutine READIWQ
SUBROUTINE READIWQ
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccc
!C This subroutine read a .IWQ file to extract the data needed to run RSE.
C
!C The data read are:
C
!C * A flag (to be used in vfsmod when RSE is used for simulation of
pollutants C
!C * 2 XML files (input [eq's included here, and output [to check indexed])
C
!C * the reaction set used (delclared in the XML input file
C
!C * number, name and data for the mobile variables (used in the reactions)
C
!C * number, name and data for the stabile variables (used in the reactions)
C
!C * number, name and data for the parameters (used in the reactions)
C
!C * Flag for reading 4 intrinsic parameters (depth, x_vel, time_step, area)
C
!C
that can be used in the equations (XML input files)
C
!C Once data are read, values are passed to the hydrodynamic driving program
C
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
191
cccc
USE aRSEDIM
USE SWIFTDIM, ONLY: NMAX,MMAX,LMAX,VARZINT
IMPLICIT NONE
INTEGER(kind=4)
integer(kind=4)
:: WQFLAG,M
:: s,i,j,k,l,n
PREPROCESS='IWQINPUT.iwq'
to being called from SETUP2
!Moved this from CALLaRSE since moving READIWQ
!Opens and read input file .iwq for RSE
OPEN (UNIT=50, FILE=PREPROCESS)
READ(50,*) WQFLAG, NMOB, NSTAB, NPAR, K_WET, ATM_NPAR
IF(NMOB.NE.LMAX)PRINT*, 'NMAX not equal to NMOB'
NVARS=NMOB+NSTAB
NCOMPS=NMOB+NSTAB+27+NPAR
CALL CELLCOUNT
CALL SUB(NMAX,MMAX,NMOB,NSTAB,NCOMPS,NCELLS)
!Read XML input file, XML outout file to check indexes, react set to be used
in XML input file
READ(50,*) XMLINPUT, XMLOUTPUT, XMLREAC_SET
!Read mobile variables
READ(50,*) (COMPNAME(i),C1_aRSE(i,1),i=1,NMOB)
!Read stabile variables
READ(50,*) (COMPNAME(j),C1_aRSE(j,1),j=(NMOB+1),(NMOB+NSTAB))
!Read stabile print flags
READ(50,*) (NPRZ(s),s=1,NSTAB)
!Equivalent to the NPRR in FTLOADDS,
but for stabile components
! Output file always has user-defined variables first (j), then 27 intrinsic
params + 1
j=NMOB+NSTAB
n=NMOB+NSTAB
k=j+27+1
j=k
!Read parameter to be used (usually declared to be used in the set of
equatiuons)
READ(50,*) (COMPNAME(k),C1_aRSE(k,1),k=j,(j+NPAR-1))
! Read intrincsic values of depth, x_vel_ol, time_step, area if m="1"
READ(50,*)M
IF(M.EQ.1) THEN
READ(50,*) COMPNAME(n+2),C1_aRSE(n+2,1)&
!depth
!&,COMPNAME(n+16),C1_aRSE(n+16,1)& !x-vel
&,COMPNAME(n+20),C1_aRSE(n+20,1)& !time
&,COMPNAME(n+1),C1_aRSE(n+1,1)
!area
ENDIF
DTaRSE=C1_aRSE(n+20,1) !time step if not in .iwq
CLOSE(50)
IF(VARZINT.NE.99)THEN
!Read in STABILE ICs as uniform
DO L=1,NSTAB
DO N=1,NMAX
DO M=1,MMAX
192
ZR(N,M,L)=C1_aRSE(NMOB+L,1)
ENDDO
ENDDO
ENDDO
ENDIF
END
Subroutine CALLaRSE
SUBROUTINE CALLaRSE
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccc
!C This program emulates a hydrodynamic calling program for using the
Reaction C
!C Simulaiton Engine (RSE). The code structure of this program can be adapted
C
!C to other hydrodynamic calling programs.
C
!C This program reads a text file (.iwq) with the data needed to used
C
!C RSE. This .iwq file contains the name of the XML input file, the name of
C
!C the XML output file to check the indexes used, the name of the reaction
set C
!C to be used (declared in the XML input file), the number(s), name(s) and
C
!C value(s) for the mobile, stabile and parameters used in the equation(s)
C
!C declared in the XML input file.
C
!C Once data is read, call MyReactionModTest subroutine, which initiate and
C
!C runs RSE.
C
!C RSE is called at each time step. Initiallitation occurs in time step 1
C
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccc
USE aRSEDIM
USE SWIFTDIM, ONLY: HALFDT,aRSE,CaRSE,NMAX,MMAX
IMPLICIT NONE
INTEGER(KIND=4) :: i,j,p,r,HALFSTEP
DATA HALFSTEP/0/
IF(INITIATE.EQ.0)THEN
CALL FORT_CSTRING(XMLINPUT, XMLINPUTC)
CALL FORT_CSTRING(XMLOUTPUT, XMLOUTPUTC)
CALL FORT_CSTRING(XMLREAC_SET,XMLREAC_SETC)
!IF (VARZINT.EQ.99) CALL READIC
DO r=1,NCELLS
DO p=1,NCOMPS
C1_aRSE(p,r)=C1_aRSE(p,1)
193
ENDDO
ENDDO
INITIATE=1
ENDIF
DO 100 CALLNO=1,NCALLS
IF(aRSE.EQ.2) THEN
HALFSTEP=HALFSTEP+1
ELSEIF(aRSE.EQ.1) THEN
HALFSTEP=HALFSTEP+2 !Initiated to zero, so +2 means always even,
so always uses R
ELSEIF(aRSE.EQ.3) THEN
HALFSTEP=1
ELSE
PRINT*, 'aRSE is neither 1, 2 or 3'
PAUSE
ENDIF
! Time step used by the controlling program
IF (DTaRSE.GT.0) THEN
DTFTLOADDS=DTaRSE
ELSEIF (aRSE.EQ.1) THEN
!time_step in RUNaRSE is DTFTLOADDS*60. If aRSE=0 then no aRSE called so the
/aRSE should
!not be a problem and acts as a check; if aRSE=1 then CaRSE is used to
specify how many full
!time-steps (HALFDT*2) to wait.
DTFTLOADDS=CaRSE*HALFDT*2
ELSEIF (aRSE.EQ.2) THEN
DTFTLOADDS=HALFDT*2/aRSE
ELSEIF (aRSE.EQ.3) THEN !use TRT split-operator
DTFTLOADDS=HALFDT*2
ENDIF
DO 10 CELLNO=1,NCELLS
IF(CELLNO.EQ.1) THEN
CALL aRSE_IN(HALFSTEP) !Halfstep needed to determine R or RP
ENDIF
CALL RUNaRSE
IF(CELLNO.EQ.NCELLS) THEN
CALL aRSE_OUT(HALFSTEP)
RP
ENDIF
10
100
CONTINUE
CONTINUE
101
FORMAT(500F8.4)
END
194
!Halfstep needed to determine R or
Subroutine aRSE_IN
SUBROUTINE aRSE_IN(HALFSTEPIN)
!********************************************************************
! This subroutine moves the necessary values into C1_aRSE for RSE
!********************************************************************
USE SWIFTDIM, ONLY:
IROCOL,NOROWS,MSTART,MEND,SEP,SEMIN,U,UP,V,VP,RP,R,LMAX,ICLSTAT,ATMDEP
USE aRSEDIM
IMPLICIT NONE
INTEGER CELLNUMI, NUMCELLSIRK, CELLNUM, IRK_aRSE, HALFSTEPIN
INTEGER M,N,L,S
REAL DEPTHMIN
DATA DEPTHMIN/0.05/
!********************************************************************
CELLNUMI=0
IF(LMAX.NE.NMOB) THEN
PRINT*,'LMAX (SWIFT2D) not equal to NMOB (aRSE)'
PAUSE
ENDIF
!*********************************************************************
!Read in mobile/transported variables from R (u-step) or RP (v-step)
!*********************************************************************
IF(HALFSTEPIN/2*2.EQ.HALFSTEPIN) THEN
!Even = v-step, which uses RP to
create R in DIFV, so use R
DO IRK_aRSE=1,NOROWS
N=IROCOL(1,IRK_aRSE)
MSTART = IROCOL(2,IRK_aRSE)
MEND = IROCOL(3,IRK_aRSE)
DO M=MSTART,MEND
CELLNUMI=CELLNUMI+1
!Mobile inputs
DO L=1,LMAX
C1_aRSE(L,CELLNUMI)=R(N,M,L)
ENDDO
!Stabile inputs
IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
IF((S.EQ.NSTAB).AND.(K_WET.EQ.1)) THEN
IF(ICLSTAT(N,M).EQ.0) THEN
!Cell is wet: K_wet=1
C1_aRSE(LMAX+S,CELLNUMI)=1
ELSEIF(ICLSTAT(N,M).NE.0) THEN
!Cell is dry: K_wet=0
C1_aRSE(LMAX+S,CELLNUMI)=0
ENDIF
ELSE
C1_aRSE(LMAX+S,CELLNUMI)=ZR(N,M,S)
ENDIF
195
ENDDO
ENDIF
!Hydro inputs
IF(ICLSTAT(N,M).NE.0) THEN
C1_aRSE(NVARS+2,CELLNUMI)=DEPTHMIN
ELSE
C1_aRSE(NVARS+2,CELLNUMI)=(SEP(N,M)-SEMIN(N,M)) !depth
ENDIF
IF(ATM_NPAR.GT.0)
C1_aRSE(NVARS+27+ATM_NPAR,CELLNUMI)=ATMDEP(2)
!C1_aRSE(NVARS+14,CELLNUMI)=U(N,M) !u-vel moved from UP to U
after u-step, not changed in v-step
!C1_aRSE(NVARS+16,CELLNUMI)=VP(N,M) !V-vel updated to VP in
SEPV earlier in v-step
ENDDO
ENDDO
ELSE
!Odd = u-step, which uses R to create RP (in DIFU) so use RP
DO IRK_aRSE=1,NOROWS
N=IROCOL(1,IRK_aRSE)
MSTART = IROCOL(2,IRK_aRSE)
MEND = IROCOL(3,IRK_aRSE)
DO M=MSTART,MEND
CELLNUMI=CELLNUMI+1
!Conc inputs
DO L=1,LMAX
C1_aRSE(L,CELLNUMI)=RP(N,M,L)
ENDDO
!Stab inputs
IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
IF((S.EQ.NSTAB).AND.(K_WET.EQ.1)) THEN
IF(ICLSTAT(N,M).EQ.0) THEN
C1_aRSE(LMAX+S,CELLNUMI)=1
ELSEIF(ICLSTAT(N,M).NE.0) THEN
C1_aRSE(LMAX+S,CELLNUMI)=0
ENDIF
ELSE
C1_aRSE(LMAX+S,CELLNUMI)=ZR(N,M,S)
ENDIF
ENDDO
ENDIF
!Hydro inputs
IF(ICLSTAT(N,M).NE.0) THEN
C1_aRSE(NVARS+2,CELLNUMI)=DEPTHMIN
ELSE
C1_aRSE(NVARS+2,CELLNUMI)=(SEP(N,M)-SEMIN(N,M)) !depth
ENDIF
IF(ATM_NPAR.GT.0)
C1_aRSE(NVARS+27+ATM_NPAR,CELLNUMI)=ATMDEP(2)
!C1_aRSE(NVARS+14,CELLNUMI)=UP(N,M) !u-vel updated to UP in
SEPU earlier in u-step
!C1_aRSE(NVARS+16,CELLNUMI)=V(N,M)
!v-vel moved from VP to
V after previous v-step, not changed in u-step
ENDDO
ENDDO
ENDIF
196
RETURN
END
Subroutine aRSE_OUT
SUBROUTINE aRSE_OUT(HALFSTEPOUT)
!********************************************************************
! This subroutine: moves the necessary values out of C1_aRSE for FTL
!********************************************************************
USE SWIFTDIM, ONLY: IROCOL,NOROWS,MSTART,MEND,RP,R,LMAX
USE aRSEDIM
IMPLICIT NONE
INTEGER CELLNUMO, NUMCELLSIRK, CELLNUM, IRK_aRSE, HALFSTEPOUT
INTEGER M,N,L,S
!********************************************************************
CELLNUMO=0
IF(LMAX.NE.NMOB) THEN
PRINT*,'LMAX (SWIFT2D) not equal to NMOB (aRSE)'
PAUSE
ENDIF
IF(HALFSTEPOUT/2*2.EQ.HALFSTEPOUT) THEN
!even = v-step, which uses RP
to create R in DIFV so use R
DO IRK_aRSE=1,NOROWS
N=IROCOL(1,IRK_aRSE)
MSTART = IROCOL(2,IRK_aRSE)
MEND = IROCOL(3,IRK_aRSE)
DO M=MSTART,MEND
CELLNUMO=CEllNUMO+1
!Mobile outputs
DO L=1,LMAX
R(N,M,L)=C1_aRSE(L,CELLNUMO)
ENDDO
!Stabile outputs
IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
ZR(N,M,S)=C1_aRSE(LMAX+S,CELLNUMO) !Use ZR always
because not transported so no ZRP
ENDDO
ENDIF
ENDDO
ENDDO
ELSE
!odd = u-step, which uses R to create RP in DIFU so use RP
DO IRK_aRSE=1,NOROWS
N=IROCOL(1,IRK_aRSE)
MSTART = IROCOL(2,IRK_aRSE)
MEND = IROCOL(3,IRK_aRSE)
DO M=MSTART,MEND
CELLNUMO=CEllNUMO+1
197
!Mobile outputs
DO L=1,LMAX
RP(N,M,L)=C1_aRSE(L,CELLNUMO)
ENDDO
!Stab outputs
IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
ZR(N,M,S)=C1_aRSE(LMAX+S,CELLNUMO) !Use ZR always
because not transported so no ZRP
ENDDO
ENDIF
ENDDO
ENDDO
ENDIF
RETURN
END
Subroutine RUNaRSE
SUBROUTINE RUNaRSE
USE IFPORT
USE aRSEDIM
IMPLICIT NONE
Integer(kind=4)
:: a,x
Integer(kind=4)
:: nvals
Integer(kind=4)
:: rk_order !Either 2 or 4
Real(kind=8)
:: time_step
Real(kind=8), Dimension(NCOMPST)
:: vars
CHARACTER (len=120)
:: input_filename,input_filename1
CHARACTER (len=120)
:: output_filename, output_filename1
CHARACTER (len=120)
:: reaction_set, reaction_set1
integer*1, Dimension (50):: input_filename1A, output_filename1A,
reaction_set1A
!REMEMBER: change Interfaces to syntax suggested by Steve on IVF forum
Interface to Subroutine Initialize ( input_xml, output_xml, rsname )
!DEC$ Attributes C, DLLIMPORT, alias: "_Initialize" :: Initialize
integer*1, Dimension (50):: input_xml, output_xml, rsname !new input
files as arrays of chars instead of strings
!
!
!
Character*(*) input_xml
'old string file name
Character*(*) output_xml
'old string file name
Character*(*) rsname
!DEC$ Attributes REFERENCE :: input_xml
!DEC$ Attributes REFERENCE :: output_xml
!DEC$ Attributes REFERENCE :: rsname
END
Interface to Subroutine PreSolve ( num_var, vars )
!DEC$ Attributes C, DLLIMPORT, alias: "_PreSolve" :: PreSolve
Integer(kind=4)
:: num_var
Real(kind=8), Dimension(num_var)
:: vars
198
End
Interface to Subroutine PostSolve ( num_var, vars )
!DEC$ Attributes C, DLLIMPORT, alias: "_PostSolve" :: PostSolve
Integer(kind=4)
:: num_var
Real(kind=8), Dimension(num_var)
:: vars
End
Interface to Subroutine RKSolve ( time_step, rk_order, num_var, vars )
!DEC$ Attributes C, DLLIMPORT, alias: "_RKSolve" :: RKSolve
Integer(kind=4)
:: num_var
Integer(kind=4)
:: rk_order
Real(kind=8)
:: time_step
Real(kind=8), Dimension(num_var)
:: vars
End
Interface to Subroutine SetGlobalValues ( num_var, vars )
!DEC$ Attributes C, DLLIMPORT, alias: "_SetGlobalValues" ::
SetGlobalValues
Integer(kind=4)
:: num_var
Real(kind=8), Dimension(num_var)
:: vars
End
nvals = NCOMPS
rk_order = RKORDER
time_step = DTFTLOADDS*60
!
Name of the input xml file (here, wq_input_file.xml)
input_filename1A = XMLINPUTC
!
Name of the component output file, only used to double check the inputs
output_filename1A = XMLOUTPUTC
!
Name of the reaction set to use - set to the same as in the input xml
file
reaction_set1A = XMLREAC_SETC
!
!
MUST initialize the passed in values to 0.0
New values of conc's are stored here @ vars
IF(INITIATE.EQ.1)THEN
DO a = 1, NCOMPS !NCOMPST
vars(a) = 0.0
ENDDO
INITIATE=2
ENDIF
DO a = 1, NCOMPS
vars(a) = C1_aRSE(a,CELLNO)
ENDDO
IF (INITIATE.EQ.2) THEN
CALL Initialize( input_filename1A, output_filename1A, reaction_set1A
)
INITIATE=3
ENDIF
CALL PreSolve(nvals, vars)
CALL RKSolve(time_step, rk_order, nvals, vars) !why nvals and not
199
num_var?
CALL PostSolve(nvals, vars)
! Nvals should be replaced with nvarX equivalent because only vars(1) and
vars(2) are changed
DO a = 1, NCOMPS
IF(a.LE.NVARS) THEN
IF(vars(a).LT.0) vars(a)=0.0
ENDIF
C1_aRSE(a,CELLNO) = vars(a)
ENDDO
20 FORMAT (I3, I3, E16.4, E16.4)
RETURN
END
Subroutine CELLCOUNT
SUBROUTINE CELLCOUNT
!********************************************************************
! This subroutine: counts the number of active cells
!********************************************************************
USE SWIFTDIM
USE aRSEDIM
IMPLICIT NONE
INTEGER NUMCELLS,NCELLSIRK,IRK_aRSE,COUNTCELLS,CELLSCOUNTED,COUNTOFF
!********************************************************************
COUNTOFF = 0
IF(COUNTOFF.EQ.1) GOTO 10
DO IRK=1,NOROWS
MSTART = IROCOL(2,IRK)
MEND = IROCOL(3,IRK)
NCELLSIRK = MEND - MSTART + 1
NUMCELLS = NUMCELLS + NCELLSIRK
ENDDO
NCELLS=NUMCELLS
10 RETURN
END
200
Section B3
READIWQ Input File
The nature of the XML interface, on which aRSE relies to obtain the names and values
of the model components (i.e. state variables and parameters), is such that aRSE relies
on the numeric order in which each component appears in order to correctly match
name and value. Given that the number of user-defined state variables and parameters
can change, so too then can the numeric reference and it is therefore necessary to run
aRSE once in order to determine what the appropriate position is for the various
components, unique to the given model setup. This is obviously undesirable for
automated calling of aRSE (and is an artifact of the parent version TaRSE) because it
requires that the user execute the model prior to using it.
This input file's purpose is to avoid the necessity for calling aRSE prior to using it, and is
predicated on the fact that the number of intrinsic parameters in the model is constant
(there are 27), that the state variables appear first in the input XML file, and that the
user-defined parameters appears last. The appropriate numeric positions of all
components can therefore be determined by knowing what and how many state
variables there are, and what and how many user-defined parameters there are. This
information is entered in this .IWQ file, read by the model, and used accordingly.
Table B-1. Explanation of the READIWQ input file structure and read in parameters
Line number
Variable
Explanation
1
WQFLAG
Flag for running water-quality module (unused)
NMOB
Number of mobile state-variables specified in input XML
NSTAB
Number of stabile state-variables specified in input XML
NPAR
Number of user-specified parameters specified in input
XML
K_WET
Flag to exchange wet/dry conditions. If used, this
parameter must be specified as the final user-input
parameter (see code in aRSE_IN subroutine)
ATM_NPAR
Flag to indicate atmospheric deposition, read in by
FTLOADDS from ATMDEP.dat input file, must be passed
to aRSE. If 0, then not, if > 0 then the input number must
correspond with the position of the parameter in the list of
user-input parameters e.g. ATM_NPAR=2 indicates that
the second nput parameter in the input XML is the
atmospheric deposition rate parameter (the name must
match that used in Line 6 of the .IWQ)
XMLINPUT
XMLOUPUT
Name of the XML input file
Name of the XML output file (not used)
2
201
Table B-1. Continued
Line number
Variable
Explanation
2
XMLREAC_SET
Name of the XML reaction set tag
3
VARNAME(i); C2(i)
For i=1 to NMOB, each mobile state-variable name must
be given (VARNAME) along with it's corresponding initial
condition (C2)
4
VARNAME(j); C2(j)
For j=NMOB to NMOB+NSTAB, each stabile state-variable
name must be given (VARNAME) along with its
corresponding initial condition (C2)
5
NPRZ(s)
For s=1 to NSTAB, the printing interval must be given.
Currently not used, but included for anologous control to
that offered by NPRR for constituent printing in SWIFT2D
6
VARNAME(k); C2(k)
For k=j+28 to j+28+NPAR, each user-specified parameter
name must be given (VARNAME) along with its
corresponding constant value (C2)
7
MM
Flag to specify whether intrinsic variables are read directly
in from .IWQ file in Line 8. If MM=1 then values read in
from Line 8
8
VARNAME(x); C2(x)
The position (x) of the desired intrinsic variable in the list of
intrinsiic parmaters must be known, and its name
(VARNAME) and value (C2) given if MM is 1
Section B4
Nash-Sutcliffe Calculation for Analytical Testing
The following program and and subroutines were written for the purpose of
calculating spatially-distributed Nash-Sutcliffe efficiencies in the comparison of
analytical and numerical solutions.
Program STUPOSTPROCESS
PROGRAM StuPOSTPROCESS
!***************************************************************************!
!
!
! PROGRAM: StuPOSTPROCESS
!
!
!
! PURPOSE: To run stats on FTLOADDSaRSE results using CORSTAT. When
!
! called, the number of measurements in the time-series to be used in the !
! statistics (TOTALTIN), and the number of cells to be assessed by rows
!
! (NMAXIN) and columns (MMAXIN)
!
!
!
202
!***************************************************************************!
USE GLOBAL
IMPLICIT NONE
integer :: err, SURFERVID,TOTALTI,YES
!Read in the number of measurements in the time-series
55
CALL GETARG(1,ARGUMENT1)
READ(ARGUMENT1,'(A6)') SURFERCASE
CALL GETARG(2,ARGUMENT2)
READ(ARGUMENT2,'(I5)') TOTALTF
CALL GETARG(3,ARGUMENT3)
READ(ARGUMENT3,'(I5)') NMAX
CALL GETARG(4,ARGUMENT4)
READ(ARGUMENT4,'(I5)') MMAX
CALL GETARG(5,ARGUMENT5)
READ(ARGUMENT5,'(I2)') SURFERVID
50 OPEN(300,FILE="C:\Users\Stuart Muller\Documents\Visual Studio
2008\Projects\FTLOADDSaRSE_v2.8\FTLOADDS_Test_Case_v3\FTLOADDS\SurferCases.tx
t",&
STATUS='REPLACE')
IF(SURFERVID.EQ.99) THEN
GOTO 100
ELSE
CALL SUB(NMAX,MMAX,TOTALTF)
TOTALT=TOTALTF
GOTO 200
ENDIF
100 DO TOTALT=2,TOTALTF
CALL SUB(NMAX,MMAX,TOTALTF)
200
IF(TOTALT.LT.10) THEN
TOTALTI=1
WRITE(SURFERSTRING1,'(I<TOTALTI>)') TOTALT
ELSEIF(TOTALT.LT.100) THEN
TOTALTI=2
WRITE(SURFERSTRING2,'(I<TOTALTI>)') TOTALT
ELSEIF(TOTALT.GE.100) THEN
TOTALTI=3
WRITE(SURFERSTRING3,'(I<TOTALTI>)') TOTALT
ENDIF
CALL POSTPROCESS
IF(SURFERVID.NE.99) GOTO 300
DEALLOCATE(C1,C2)
203
ENDDO
300 CONTINUE
END PROGRAM StuPOSTPROCESS
Subroutine POSTPROCESS
SUBROUTINE POSTPROCESS
USE GLOBAL
!C***************************************************************************
********
! This subroutine combines the prepared results from FTLOADDSaRSE
(LCONR1_AN.txt)
!
! and 3DADE (CXTFIT.OUTe) into CORSTAT.TXT for statistical processing
!
!****************************************************************************
*******!
IMPLICIT NONE
CHARACTER*50 MODELFILE,MODFILE,ANALFILE,ANALYTFILE
INTEGER t,i,j !!,TOTALT,NMAX,MMAX
!Input files must be of the format INTEGER, REAL(OBS), REAL(SIM)
!The integer is the code for a given time series of data (NCOD in CORSTAT),
and increments up when a new series is encountered (this
!is not used currently)
MODELFILE='..\output\LCONR1_AN.txt'
OPEN(100,FILE=MODELFILE,STATUS='OLD')
ANALYTFILE='..\output\CXTFIT.OUTe'
OPEN(101,FILE=ANALYTFILE,STATUS='OLD')
DO t=1,TOTALT
DO j=1,MMAX
DO i=1,NMAX
READ(100,'(F8.4)',END=1010) C1(i,j,t)
outputs
READ(101,'(F8.4)',END=1010) C2(i,j,t)
model outputs
ENDDO
ENDDO
ENDDO
PRINT*, "Reads complete"
!pause
GOTO 1011
!Read in model
!Read in analytical
1010PRINT*, "Specified time-series exceeds either observed or simulated data
input"
204
1011CONTINUE
1020CONTINUE
DO j=1,MMAX
DO i= 1,NMAX
CALL CORSTAT(i,j,TOTALT)
ENDDO
ENDDO
1008FORMAT(I3,F8.4,1X,F8.4)
PRINT*, 't:',t,'m:',j,'n:',i
END
Subroutine CORSTAT
SUBROUTINE CORSTAT(NN,MM,TOTALI)
!C************************************************************************
!C*
WRITTEN FOR: Paper on VFSMOD development and testing (J.of Hyd) *
!C*
Last Updated:June 29, 1998.
*
!C*
CORSTAT, 5/20/87, VER. 0.1, J.E. PARSONS
*
!C*
REVISED: 5/11/93, VER, 0.3, R. MUNOZ-CARPENA
*
!C*
UPDATED: 06/04/02, VER, 0.7, R. MUNOZ-CARPENA
*
!C*
e-mail: carpena@ufl.edu
*
!C*
ADAPTED: 2/7/10 S. MULLER (!SJM) for FTLOADDSaRSE
*
!C*
CREDITS: (c) 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
*
!C*
USES:(c)Numerical recipes: tptest, avevar, betai,gammaln, betacf *
!ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
!C*
CORSTAT, 5/20/87, VER. 0.1, J.E. PARSONS
*
!C*
REVISED: 5/11/93, VER, 0.3, R. MUNOZ-CARPENA
*
!C*
LAST UPDATED: 29/6/98, VER, 0.5, R. MUNOZ-CARPENA
*
!C*
THIS PROGRAM COMPUTES A NUMBER OF STATISTICS FOR THE
*
!C*
COMPARISON OF TWO TIME SERIES, FOR EXAMPLE, AN OBSERVED AND A
*
!C*
SIMULATED ONE.
THE STATISTICS ARE:
*
!C*
1) MEAN ERROR
*
!C*
2) STANDARD DEVIATION
*
!C*
3) SERIAL CORELATION COEF.
*
!C*
4) COEFICIENT OF PERFORMANCE
*
!C*
5) COEFICIENT OF PERFORMANCE CORRECTED FOR VARIATION OF THE
*
!C*
OF THE RECORDED PROCESS
*
!C*
6) PEARSON MOMENT AND THE WEIGHTED MOMENT
*
!C* RMC-7) Correlation coefficient for the 1:1 line
*
!C* RMC-8) Paired t-test to check for differences in series means
*
!C*
(from Numerical Recipes)
*
!C*
*
!C*
These are computed for the absolute value of the error and the
*
!C*
error.
*
!C*
These measures are defined and discussed in:
*
!C*
*
!C* 1. Aitken, A.P. 1973. Assesing systematic errors in rainfall-runoff *
205
!C*
models. J. of Hydrology. 20:121-136.
*
!C* 2. James, L.D. and S.J. Burges. 1982. Selection, calibration, and
*
!C*
testing of hydrologic models by. In Hydrologic Modeling of Small *
!C*
Watersheds, Chapter 11, ed. C. T. Haan, H. P. Johnson and D. L. *
!C*
Brakensiek. pages 435-472. ASAE monograph no. 5. St. Joseph.
*
!C* 3. McCuen, R.H. and W.M. Snyder. 1975. A proposed index for
*
!C*
comparing hydrographs. Water Resour. Res. (AGU).11(6):1021-1024. *
!C* 4. Press et al., 1992. Numerical Recipes in Fortran. 2nd, edition.
*
!C*
Cambridge: Cambridge University Press
*
!C*
*
!C*
Definition of variables
*
!C************************************************************************
USE GLOBAL, ONLY:
C1,C2,SURFERSTRING1,SURFERSTRING2,SURFERSTRING3,TOTALT,SURFERCASE
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
character*16 dummyf1
CHARACTER*6 VARBLE
CHARACTER*50 FLABEL
PARAMETER(NPTS=500)
REAL prob1,t1,data1(NPTS),data2(NPTS)
DIMENSION NCOD(5000),OBS(5000),SIM(5000),AERR(5000),&
ERR(5000),NCD(101),NTC(101),SUM(4),SUMSQ(4),CSS(4),DAERR(1000),&
DREC(1000),VAR(4)
INTEGER MM,NN,TOTALI,FILELABELS,ALLOCATEARRAY
DATA FILELABELS/0/
DATA ALLOCATEARRAY/0/
OPEN (UNIT=10,FILE='NUL')
IDIAG=0
I=1
INC=0
KC=0
NC=0
mycount=0
!SJM: Removing FLABEL read because CORSTATIN.txt not being written with
headers
!READ(8,*)FLABEL
!10 READ(8,*,END=20)NCOD(I),OBS(I),SIM(I)
!SJM: Instead of a READ now transferring data between arrays. Note, still
jumps to 20
!when OBS and SIM are filled
DO I=1,TOTALI
NCOD(I)=1
!!OBS(I)=OBSC1(NN,MM,I)
OBS(I)=C1(NN,MM,I)
!!SIM(I)=SIMC2(NN,MM,I)
SIM(I)=C2(NN,MM,I)
!c-- Debug
---!c
print*,ncod(i),obs(i),sim(i)
!c-- End Debug ---ERR(I)=SIM(I)-OBS(I)
AERR(I)=DABS(ERR(I))
206
!C*** COUNT THE DIFFERENT CODES
IF (NC.EQ.NCOD(I)) THEN
INC=INC+1
NTC(KC)=INC
ELSE
KC=KC+1
NC=NCOD(I)
NCD(KC)=NC
INC=1
ENDIF
!SJM: Deleted because DO loop automatically updates I
!
I=I+1
ENDDO
20 CONTINUE
!C** ZERO OUT THE STATISTICS ARRAYS
NOBS=I
IST=1
DO 25 K=1,KC
DO 24 J=1,4
SUM(J)=0.D0
SUMSQ(J)=0.D0
24
CONTINUE
CROSS=0.D0
cosse=0.d0
NOBK=NTC(K)+IST-1 !!!!!!!!!!!!!GRRR
KOUNT=0
DO 30 I=IST,NOBK
KOUNT=KOUNT+1
DAERR(KOUNT)=AERR(I)
DREC(KOUNT)=OBS(I)
SUM(1)=SUM(1)+ERR(I)
SUM(2)=SUM(2)+AERR(I)
SUM(3)=SUM(3)+OBS(I)
SUM(4)=SUM(4)+SIM(I)
SUMSQ(1)=SUMSQ(1)+ERR(I)*ERR(I)
SUMSQ(2)=SUMSQ(2)+AERR(I)*AERR(I)
SUMSQ(3)=SUMSQ(3)+OBS(I)*OBS(I)
SUMSQ(4)=SUMSQ(4)+SIM(I)*SIM(I)
CROSS=CROSS+OBS(I)*SIM(I)
cosse=cosse+(obs(i)-sim(i))*(obs(i)-sim(i))
data1(KOUNT)=OBS(I)
data2(KOUNT)=SIM(I)
30
CONTINUE
mycount=mycount+1
XPOINT=DFLOAT(NTC(K))
ERMEAN=SUM(1)/XPOINT
AEMEAN=SUM(2)/XPOINT
OBMEAN=SUM(3)/XPOINT
SIMEAN=SUM(4)/XPOINT
!C*** DO RESIDUAL MASS CURVES FOR ACCUMMULATED ERRORS
CPAT=0
CPBT=0
CPCT=0
SECOR=0.D0
SAECOR=0.D0
DO 37 I=IST,NOBK
IF (I.GT.IST) THEN
207
SECOR=SECOR+(ERR(I)-ERMEAN)*(ERR(I-1)-ERMEAN)
SAECOR=SAECOR+(AERR(I)-AEMEAN)*(AERR(I-1)-AEMEAN)
ENDIF
ERS=0.D0
ERD=0.D0
ERD2=0.D0
DO 36 II=IST,I
ERS=ERS+ERR(II)
ERD=ERD+OBS(II)
ERD2=ERD2+(OBS(II)-OBMEAN)
36
CONTINUE
XJP=DFLOAT(I-IST+1)
XJP2=XJP*XJP
CPAT=CPAT+ERS*ERS/XJP2
CPBT=CPBT+(ERS/ERD)*(ERS/ERD)/XJP2
!c
CPCT=CPCT+(ERS/ERD2)*(ERS/ERD2)/XJP2
37
CONTINUE
!C
CPAT=CPAT/XPOINT
!C
CPBT=CPBT/XPOINT
!C
CPCT=CPCT/XPOINT
IST=NOBK+1
IF (IDIAG.EQ.1) THEN
WRITE(10,90)XPOINT,K,NCD(K)
90
FORMAT(/,/,/,10X,'***** DIAGNOSTICS PRIOR TO CALCULATIONS FOR:',&
/,20X,'NPOINTS=',I6,' SERIES NO.=',I4,' SERIES CODE=',I5,&
/,10X,'SUM OF DATA',10X,'SUM OF SQUARES')
DO 91 KK=1,4
WRITE(10,89)SUM(KK),SUMSQ(KK)
89
FORMAT(5X,F15.5,9X,F15.5)
91
CONTINUE
WRITE(10,88)CROSS
88
FORMAT(/,10X,'CROSS PRODUCT SUM (REC*SIM)=',F15.5,/,/)
ENDIF
CSS(1)=SUMSQ(1)-2*ERMEAN*SUM(1)+XPOINT*ERMEAN*ERMEAN
CSS(2)=SUMSQ(2)-2*AEMEAN*SUM(2)+XPOINT*AEMEAN*AEMEAN
CSS(3)=SUMSQ(3)-2*OBMEAN*SUM(3)+XPOINT*OBMEAN*OBMEAN
CSS(4)=SUMSQ(4)-2*SIMEAN*SUM(4)+XPOINT*SIMEAN*SIMEAN
VAR(1)=CSS(1)/XPOINT
VAR(2)=CSS(2)/XPOINT
VAR(3)=CSS(3)/XPOINT
VAR(4)=CSS(4)/XPOINT
XP1=(XPOINT-1.D0)
SEM=CSS(1)/(XP1)
AEM=SUM(2)/XPOINT
!c
RMSE=DSQRT(CSS(1)/XPOINT)
!c----change based on Marlon's comments (07/06/93)---------RMSE=DSQRT(SUMSQ(1)/XPOINT)
ERSTD=DSQRT(CSS(1)/(XP1))
AESTD=DSQRT(CSS(2)/(XP1))
OBSTD=DSQRT(CSS(3)/(XP1))
SISTD=DSQRT(CSS(4)/(XP1))
SECOR=SECOR/(ERSTD*ERSTD*(XP1))
SAECOR=SAECOR/(AESTD*AESTD*(XP1))
!c -rmc-06/02--!c
RPEARM=(CROSS-OBMEAN*SUM(4)-SIMEAN*SUM(3)
!c
! + XPOINT*OBMEAN*SIMEAN)/(OBSTD*SISTD*XPOINT)
RPEARM=(XPOINT*CROSS-SUM(4)*SUM(3))/SQRT((XPOINT*SUMSQ(3)-SUM(3)*&
208
SUM(3))*(XPOINT*SUMSQ(4)-SUM(4)*SUM(4)))
R2PEAR=RPEARM*RPEARM
W=SISTD/OBSTD
IF (W.GT.1.D0) THEN
WGHTRP=RPEARM/W
ELSE
WGHTRP=RPEARM*W
ENDIF
CPAP=1.D0-SUMSQ(1)/CSS(3)
SLPNI=CROSS/SUMSQ(3)
SLPI=(CROSS-SUM(3)*SUM(4)/XPOINT)/(SUMSQ(3)-SUM(3)*SUM(3)/XPOINT)
YINT=SIMEAN-SLPI*OBMEAN
CORI=SLPI*OBSTD/SISTD
!C*** EJS --- R-SQUARED TO MATCH SAS
SSINT=SUM(4)*SUM(4)/XPOINT
EJDEN1=SUMSQ(3)-SUM(3)*SUM(3)/XPOINT
EJDEN2=SUMSQ(4)-SUM(4)*SUM(4)/XPOINT
EJSNUM=(CROSS-SUM(3)*SUM(4)/XPOINT)
SSB1B0=SLPI*EJSNUM
RESID=SUMSQ(4)-SSINT-SSB1B0
EMSRES=RESID/(XPOINT-2.D0)
STESLP=DSQRT(EMSRES/EJDEN1)
STEINT=DSQRT(EMSRES*SUMSQ(3)/(XPOINT*EJDEN1))
!C*** COMPUTATIONS FOR NO INT ?
SSB1=SLPNI*EJSNUM
RESNI=SUMSQ(4)-SSB1
EMSRNI=RESNI/(XPOINT-1.D0)
SESLPN=DSQRT(EMSRNI/EJDEN1)
CD=SSB1/EJDEN2
CALL GMEDN(KOUNT,DAERR,DREC,OBMEAN,R29)
R21TOP=SUMSQ(3)-2.D0*CROSS+SUMSQ(4)
R21=1.D0 - R21TOP/CSS(3)
R22TOP=SUMSQ(4)-2.D0*SUM(4)*OBMEAN+ XPOINT*OBMEAN*OBMEAN
R22=R22TOP/CSS(3)
R23=CSS(4)/CSS(3)
R24=1.D0 - CSS(1)/CSS(3)
R27=1.D0 - R21TOP/SUMSQ(3)
!c
print*,obstd,covaryyc
R28=SUMSQ(4)/SUMSQ(3)
100
WRITE(10,100)NCD(K),XPOINT
FORMAT(/,10X,&
'SUMMARY STATISTICS FOR COMPARING TWO SERIES OF OBSERVED vs.',&
' PREDICTED VALUES',/,10X,'SERIES CODE =',I4,10X,&
'NUMBER OF SERIES POINTS=',F6.0,/)
WRITE(10,*)'
VARIABLE
SUM
MEAN
SUMSQ&
CORR. SS
SAMP.STD.
VARIANCE
COEF. OF VAR.'
WRITE(10,*)
VARBLE='ERROR'
CV=ERSTD/ERMEAN
WRITE(10,102)VARBLE,SUM(1),ERMEAN,SUMSQ(1),CSS(1),ERSTD,VAR(1),CV
VARBLE='AERROR'
CV=AESTD/AEMEAN
WRITE(10,102)VARBLE,SUM(2),AEMEAN,SUMSQ(2),CSS(2),AESTD,VAR(2),CV
VARBLE='OBSED'
CV=OBSTD/OBMEAN
WRITE(10,102)VARBLE,SUM(3),OBMEAN,SUMSQ(3),CSS(3),OBSTD,VAR(3),CV
209
VARBLE='SIMED'
CV=SISTD/SIMEAN
WRITE(10,102)VARBLE,SUM(4),SIMEAN,SUMSQ(4),CSS(4),SISTD,VAR(4),CV
!c 102 FORMAT(5X,A6,5X,E12.3,5X,e11.4,5X,e15.4,5X,e11.4,5X,e10.5,
!c
!
5X,e10.5,5X,e11.4)
102
FORMAT(5X,A6,E14.4,e14.4,e14.4,e14.4,e14.4,e14.4,e14.4)
WRITE(10,103)RPEARM,WGHTRP,R2PEAR,R21,R22,R23,R24,R27,R28,R29
WRITE(10,105)RMSE,AEM,SEM
103
FORMAT(/,/,5X,'***** CORREL. COMPARISONS ******',&
/,15X,'PEARSON MOMENT
=',F10.5,' (FIRST TWO CORREL. TYPES)',&
/,15X,'WGHTED PEAR. MOM. =',F10.5,' (EQN 11.13)',&
/,15X,'PEAR. MOM. SQUAR. =',F10.5,' (KVALSETH R25, R26 MULT. R)',&
' (NOTE: FROM HERE DOWN R-SQUARED TYPES)',&
/,15X,'KVALSETH R21
=',F10.5,' (0<=R21<=1, GENERALLY)',&
'
(1 - RATIO OF SUM (OBS-SIM)**2/ CSS-OBS)',&
/,15X,'KVALSETH R22
=',F10.5,' (MAY EXCEED 1)',&
'
( RATIO OF SUM (SIM-OBMEAN)**2/ CSS-OBS)',&
/,15X,'KVALSETH R23
=',F10.5,' (MAY EXCEED 1)',&
'
( RATIO OF CSS-SIM/ CSS-OBS)',&
/,15X,'KVALSETH R24
=',F10.5,' (0<=R24<=1, GENERALLY)',&
'
(1 - RATIO OF CSS-ERR/ CSS-OBS)',&
/,15X,'KVALSETH R27
=',F10.5,' (RECOMMEND LINEAR NOINT.)',&
'
(1 - RATIO OF SUM ERR**2/ SUM OBS**2)',&
/,15X,'KVALSETH R28
=',F10.5,' (RECOMMEND LIN. NOINT.)',&
'
( R28 MAY EXCEED 1, RATIO OF SUM SIM**2/ SUM OBS**2)',&
/,15X,'KVALSETH R29
=',F10.5,' (RESISTANT OR ROBUST FIT)')
105
FORMAT(15X,'ROOT MEAN SQ. ERR.=',E14.5,' [(OBS-SIM)**2/N)**.5]',&
/,15X,'MEAN ABS. ERROR
=',E14.5,&
/,15X,'MEAN SQ. ERROR
=',E14.5,' (ASS. ONE MODEL PARAMETER)',&
'
[(OBS-SIM)**2/(N-1)]')
WRITE(10,104)CPAP,SECOR,SAECOR
104
FORMAT(15X,'COEF. OF EFF. (NASH AND SUTCLIFF) =',F15.5,&
'
(RATIO SS-ERR/ CSS-OBS)',/,&
15X,'SERIAL CORR. (ERROR)
=',F10.5,5X,'LAG 1',&
/,15X,'SERIAL CORR. (ABS. ERROR)=',F10.5,5X,'LAG 1')
!SJM: Write results for graphing in Surfer
!@!IF(SURFERVID.EQ.99) THEN !Calculating stats at multiple time to
make a video
IF(TOTALT.LT.10) THEN
OPEN(1100+TOTALT,FILE='Surfer'//SURFERCASE//'_T'//SURFERSTRING1//'.dat')
ELSEIF(TOTALT.LT.100) THEN
OPEN(1100+TOTALT,FILE='Surfer'//SURFERCASE//'_T'//SURFERSTRING2//'.dat')
ELSEIF(TOTALT.GE.100) THEN
OPEN(1100+TOTALT,FILE='Surfer'//SURFERCASE//'_T'//SURFERSTRING3//'.dat')
ENDIF
!Print one line of headers
IF(FILELABELS.EQ.0) THEN
WRITE(1100+TOTALT,'(2A5,4A12)') "X", "Y", "RMSE", "AEM",
"SEM", "CPAP(N-S)"
FILELABELS=1
ENDIF
210
IF(CPAP.NE.CPAP) CPAP=10
WRITE(1100+TOTALT,'(2I5,4F12.8)') MM,NN,RMSE,AEM,SEM,CPAP
IF(CPAP.NE.CPAP) CPAP=10
WRITE(1100,'(2I5,4F10.4)') MM,NN,RMSE,AEM,SEM,CPAP
WRITE(10,106)CPAT,CPBT
,CPCT
106
FORMAT(/,/,5X,'****** RESIDUAL MASS CURVES (ACCUMULATED ERRORS)',&
' DIVIDED BY NPOINTS, SIMILAR TO A VARIANCE',&
/,15X,'CPAT -- EQN 11.31 =',G13.6,&
/,15X,'CPBT -- EQN 11.32 =',G13.6,/)
!c ! /,15X,'CPCT -- EQN 11.33 =',G13.6,/)
CORI2=CORI*CORI
WRITE(10,109)SLPNI,CD,SESLPN,SLPI,YINT,CORI,CORI2,STESLP,STEINT
109
FORMAT(/,/,5X,'****** REGRESSION ANALYSIS SIM VS OBS *******',&
/,10X,'NO-INTERCEPT MODEL, SLOPE =',F10.5,'
JPR-RSQ?=',F10.5,&
'
JPSTD. ERR. SLP.?=',F10.5,&
/,10X,'INTERCEPT MODEL, SLOPE
=',F10.5,' INTERCEPT=',F10.5,&
'
CORRELATION COEF.=',F8.5,' CORR**2=',F8.5,&
/,25X,'STD. ERR. SLOPE =',F10.5,'
STD. ERR. INT. =',F10.5)
!c
!c--rmc----04/93---Error over the 1:1 line, observed vs. predicted --------WRITE(10,*)
WRITE(10,*)
WRITE(10,*)'
****** ERROR MEASURE FROM THE 1:1 LINE ********'
!c --rmc and arr 06/02--- R2= 1-RSSmodel/RSSnull model, where RSS=res. sum
sq.
!c -- null model= line y=cte=ymean=obs_mean; model = 1:1 line = y=x ->
pred=obs
!c -- old-- covaryyc=dsqrt(cosse/(xpoint-2.d0))
113
114
covaryyc=dsqrt(cosse/(xpoint-1.d0))
rsq1to1=(1.d0-(covaryyc*covaryyc)/(obstd*obstd))
if(rsq1to1.lt.0)rsq1to1=0
r1to1=dsqrt(rsq1to1)
if(rsq1to1.gt.0) then
WRITE(10,113)covaryyc,r1to1,rsq1to1
else
WRITE(10,114)covaryyc
endif
format(10x,'1:1 COVARIANCE OBSERVED vs. PREDICTED = ',E14.4,&
/,10X,'1:1 SAMPLE COEFFICIENT OF DETERMINATION (R1:1) = ',f10.4,&
/,10x,'1:1 SAMPLE CORRELATION COEFFICIENT
(RSQ1:1) = ',f10.4)
format(10x,'1:1 COVARIANCE OBSERVED vs. PREDICTED = ',E14.4,&
/,10X,'1:1 SAMPLE COEFFICIENT OF DETERMINATION (R1:1) < 0.01',&
/,10x,'1:1 SAMPLE CORRELATION COEFFICIENT
(RSQ1:1) < 0.01')
!C-------------------------------------------------------------------!c--rmc----06/98---Paired t-test --------WRITE(10,*)
WRITE(10,*)
WRITE(10,*)'
****** PAIRED t-TEST ********'
call tptest(data1,data2,KOUNT,t1,prob1)
if(prob1.ge..05) then
WRITE(10,120)NCD(K),KOUNT,t1,prob1
211
else
120
121
WRITE(10,121)NCD(K),KOUNT,t1,prob1
endif
t1=0.
prob1=0.
format(10x,'No. Series= ',i4,'; n= ',i4,'; t= ',f10.6,&
'; Prob= ',f10.4,' Means not significantly different')
format(10x,'No. Series= ',i4,'; n= ',i4,'; t= ',f10.6,&
'; Prob= ',f10.4,' * Means significantly different')
WRITE(10,111)
FORMAT(/,125('-'))
WRITE(10,112)
112
FORMAT('1')
25 CONTINUE
CLOSE(8)
RETURN
END
111
SUBROUTINE GMEDN(N,ER,REC,RECM,R29)
!C**** COMPUTATION OF MEDIANS FOR R29 FROM KVALSETH
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION ER(*),REC(*),TER(1000),DREC(1000)
DO 5 I=1,N
TER(I)=ER(I)
DREC(I)=DABS(REC(I)-RECM)
5
CONTINUE
DO 10 I=1,N
DO 9 J=I+1,N
IF (TER(J).LT.TER(I)) THEN
TEM=TER(I)
TER(I)=TER(J)
TER(J)=TEM
ENDIF
IF (DREC(J).LT.DREC(I)) THEN
TEM=DREC(I)
DREC(I)=DREC(J)
DREC(J)=TEM
ENDIF
9
CONTINUE
10 CONTINUE
IMED=N/2
DRM=DREC(IMED)
ERM=TER(IMED)
RAT=ERM/DRM
R29=1.D0-RAT*RAT
RETURN
END
SUBROUTINE tptest(data1,data2,n,t,prob)
INTEGER n
REAL prob,t,data1(n),data2(n)
!CU
USES avevar,betai
INTEGER j
REAL ave1,ave2,cov,df,sd,var1,var2,betai
!c--rmc!c
write(*,*)n,t,prob
212
!c
do 5 i=1,n
!c
WRITE(*,*)data1(i),data2(i)
!c5
continue
!c--rmccall avevar(data1,n,ave1,var1)
call avevar(data2,n,ave2,var2)
cov=0.
do 11 j=1,n
cov=cov+(data1(j)-ave1)*(data2(j)-ave2)
11 continue
df=n-1
cov=cov/df
sd=sqrt((var1+var2-2.*cov)/n)
t=(ave1-ave2)/sd
prob=betai(0.5*df,0.5,df/(df+t**2))
return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
SUBROUTINE avevar(data,n,ave,var)
INTEGER n
REAL ave,var,data(n)
INTEGER j
REAL s,ep
ave=0.0
do 11 j=1,n
ave=ave+data(j)
11 continue
ave=ave/n
var=0.0
ep=0.0
do 12 j=1,n
s=data(j)-ave
ep=ep+s
var=var+s*s
12 continue
var=(var-ep**2/n)/(n-1)
return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
FUNCTION betacf(a,b,x)
INTEGER MAXIT
REAL betacf,a,b,x,EPS,FPMIN
PARAMETER (MAXIT=100,EPS=3.e-7,FPMIN=1.e-30)
INTEGER m,m2
REAL aa,c,d,del,h,qab,qam,qap
qab=a+b
qap=a+1.
qam=a-1.
c=1.
d=1.-qab*x/qap
if(abs(d).lt.FPMIN)d=FPMIN
d=1./d
h=d
do 11 m=1,MAXIT
m2=2*m
aa=m*(b-m)*x/((qam+m2)*(a+m2))
d=1.+aa*d
213
11
if(abs(d).lt.FPMIN)d=FPMIN
c=1.+aa/c
if(abs(c).lt.FPMIN)c=FPMIN
d=1./d
h=h*d*c
aa=-(a+m)*(qab+m)*x/((a+m2)*(qap+m2))
d=1.+aa*d
if(abs(d).lt.FPMIN)d=FPMIN
c=1.+aa/c
if(abs(c).lt.FPMIN)c=FPMIN
d=1./d
del=d*c
h=h*del
if(abs(del-1.).lt.EPS)goto 1
continue
1
betacf=h
return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
FUNCTION betai(a,b,x)
REAL betai,a,b,x
!CU
USES betacf,gammln
REAL bt,betacf,gammln
if(x.lt.0..or.x.gt.1.)pause 'bad argument x in betai'
if(x.eq.0..or.x.eq.1.)then
bt=0.
else
bt=exp(gammln(a+b)-gammln(a)-gammln(b)+a*log(x)+b*log(1.-x))
endif
if(x.lt.(a+1.)/(a+b+2.))then
betai=bt*betacf(a,b,x)/a
return
else
betai=1.-bt*betacf(b,a,1.-x)/b
return
endif
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
FUNCTION gammln(xx)
REAL gammln,xx
INTEGER j
DOUBLE PRECISION ser,stp,tmp,x,y,cof(6)
SAVE cof,stp
DATA cof,stp/76.18009172947146d0,-86.50532032941677d0,&
24.01409824083091d0,-1.231739572450155d0,.1208650973866179d-2,&
-.5395239384953d-5,2.5066282746310005d0/
x=xx
y=x
tmp=x+5.5d0
tmp=(x+0.5d0)*log(tmp)-tmp
ser=1.000000000190015d0
do 11 j=1,6
y=y+1.d0
ser=ser+cof(j)/y
11 continue
gammln=tmp+log(stp*ser/x)
214
!C
return
END
(C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
215
APPENDIX C
WATER-QUALITY APPLICATION CODE AND INPUT FILES
Section C1
Additional Subroutines for Water-Quality Inputs
The following two subroutines were required for input of water-quality boundary
conditions. The subroutine EDIT_INPUTFILE is used to edit time-series concentrations
at specified head boundaries in the Part 3 of the SWIFT2D input file. The subroutine
STRUNCTCONCS reads in discharge source concentrations from the
INPUTFLOWCONCS.dat input file (see Section C2).
Subroutine EDIT_INPUTFILE
PROGRAM Edit_inputfile
IMPLICIT NONE
INTEGER X,COUNT1,COUNT2,i,j,NTCT1,LENGTH,DAY,DAYCHK,P3_READ,DAYMAX
REAL TITI
CHARACTER THE_REST*60,TEMP*1050,THE_REST_19*19
CHARACTER*7 BC1(500),BC2(500),BC3(500),BC4(500)
DATA X,COUNT1,COUNT2,P3_READ,DAYMAX/0,0,0,0,0/
OPEN(10,FILE='wetlands_PBC_SICS.inp')
OPEN(20,FILE='wetlands.inp')
OPEN(30,FILE='BC_concs.inp')
!original .inp
!.inp produced by this code
!source for BC concs
j=0
DO WHILE (X.EQ.0)
j=j+1
READ(30,*,END=100) DAYCHK,BC1(j),BC2(j),BC3(j),BC4(j)
WRITE(40,'(I4,1X,A8,1X,A8,1X,A8,1X,A8,1X)')
DAYCHK,BC1(j),BC2(j),BC3(j),BC4(j)
ENDDO
!
100 CONTINUE
!******************************!
! Write PART 1 and PART 2 data !
!******************************!
DO i=1,1158 !1133 !Look at the .inp file to see what the row number is up
to Part 3 data
IF(i.GE.806.AND.i.LE.903) THEN
READ(10,'(A1050)') TEMP
ELSE
READ(10,'(A100)') TEMP
216
ENDIF
LENGTH=LEN_TRIM(TEMP)
WRITE(20,'(A<LENGTH>)') TEMP
ENDDO
PAUSE
!READ(10,'(A100)') TEMP
!PRINT*, TEMP
!PAUSE
DO WHILE (X.EQ.0)
READ(10,'(I1,A39)') NTCT1,THE_REST
LENGTH=LEN_TRIM(THE_REST)
IF(NTCT1.EQ.0) P3_READ=P3_READ+1
DAY=P3_READ/96+1
IF(DAY.GE.499) DAYMAX=1 !498 days of BC input data - after day 498
completed then just copy and repeat remaining lines.
IF(DAYMAX.EQ.1) GOTO 110
IF(NTCT1.EQ.0) THEN
WRITE(20,'(I1,A<LENGTH>)') NTCT1,THE_REST
ELSEIF(NTCT1.EQ.1) THEN
THE_REST_19=THE_REST
COUNT1=COUNT1+1
IF(COUNT1.LE.4) THEN
IF(COUNT1.EQ.1) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC1(DAY)
IF(COUNT1.EQ.2) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC2(DAY)
IF(COUNT1.EQ.3) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC3(DAY)
IF(COUNT1.EQ.4) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC4(DAY)
ELSEIF(COUNT1.LE.8) THEN
WRITE(20,'(I1,A19,A8)') NTCT1,THE_REST,'
0.005'
IF(COUNT1.EQ.8)COUNT1=0
ENDIF
ELSEIF(NTCT1.EQ.2) THEN
THE_REST_19=THE_REST
COUNT2=COUNT2+1
IF(COUNT2.LE.4) THEN
IF(COUNT2.EQ.1) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC1(DAY)
IF(COUNT2.EQ.2) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC2(DAY)
IF(COUNT2.EQ.3) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC3(DAY)
IF(COUNT2.EQ.4) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE_REST_19,BC4(DAY)
ELSEIF(COUNT2.LE.8) THEN
WRITE(20,'(I1,A19,A8)') NTCT1,THE_REST,'
0.005'
IF(COUNT2.EQ.8)COUNT2=0
ENDIF
ELSEIF(NTCT1.GT.2) THEN
WRITE(20,'(I1,A<LENGTH>)') NTCT1,THE_REST
ENDIF
110
IF(DAYMAX.EQ.1) THEN
IF(NTCT1.EQ.0) WRITE(20,'(I1,A<LENGTH>)') NTCT1,THE_REST
IF((NTCT1.EQ.1).OR.(NTCT1.EQ.2)) WRITE(20,'(I1,A<LENGTH>)')
217
NTCT1,THE_REST
IF(NTCT1.GT.2) WRITE(20,'(I1,A<LENGTH>)') NTCT1,THE_REST
ENDIF
ENDDO
END PROGRAM Edit_inputfile
Subroutine STRUCTCONCS
SUBROUTINE STRUCTCONCS
USE SWIFTDIM
USE COUPLING
REAL*4 DAY !STRCFLOWCONC(40),STRCFLOWCONC2(40) - moved to SWIFTDIM
REAL*8 DAYCHK
DATA IFIRST/1/,IUSFLOWCONCS/175/
IF(IFIRST .EQ. 1)THEN
OPEN(IUSFLOWCONCS,FILE='..\Input\FLOWS\INPUTFLOWCONCS.DAT',
1
STATUS='OLD',ACCESS='SEQUENTIAL')
READ(IUSFLOWCONCS,*) NUMSTRUCS
NUMSTRUCS=NUMSTRUCS+1
DO J=2,NUMSTRUCS
READ(IUSFLOWCONCS,*) NFLWPTS(J),NRANGES(J)
DO I=1,NFLWPTS(J)+2*NRANGES(J)
READ(IUSFLOWCONCS,*) MSTRUC(J,I),NSTRUC(J,I),IXYFLOW(J,I)
ENDDO
NTOTPTS(J)=NFLWPTS(J)
IF(NRANGES(J).GT.0) THEN
DO I=NFLWPTS(J)+1,NFLWPTS(J)+2*NRANGES(J)-1,2
IP1=I+1
MSTRUC(J,IP1)=MSTRUC(J,IP1)-MSTRUC(J,I)
NSTRUC(J,IP1)=NSTRUC(J,IP1)-NSTRUC(J,I)
IF(ABS(MSTRUC(J,IP1)).GT.ABS(NSTRUC(J,IP1)))NSTRUC(J,IP1)=0
IF(ABS(NSTRUC(J,IP1)).GT.ABS(MSTRUC(J,IP1)))MSTRUC(J,IP1)=0
MAXMN=MAX(ABS(MSTRUC(J,IP1)),ABS(NSTRUC(J,IP1)))+1
NTOTPTS(J)=NTOTPTS(J)+MAXMN
ENDDO
ENDIF
ENDDO
!If more than one solute (excl salinity and temp) then need to have
one line in inputfile for each L
!for each day,
!e.g. Line1: Day1 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3)
!
Line2: Day1 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3)
!
Line3: Day2 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3)
!
Line4: Day2 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3)
DO L=1,LMAX
IF(L.EQ.LSAL)GOTO 115 !Skip salinity and temp so don't have to add
these to input file
IF(L.EQ.LTEMP)GOTO 115
READ(IUSFLOWCONCS,*)(STRCFLOWCONC(L,J), J=1,NUMSTRUCS) !Assumes 1
solute
115
CONTINUE
ENDDO
DO L=1,LMAX
IF(L.EQ.LSAL)GOTO 116 !Skip salinity and temp so don't have to add
218
these to input file
IF(L.EQ.LTEMP)GOTO 116
READ(IUSFLOWCONCS,*)(STRCFLOWCONC2(L,J), J=1,NUMSTRUCS)
!Assumes
1 solute
116
CONTINUE
ENDDO
IFIRST=0
ENDIF
C * * SECTION EXECUTED EVERY TIMESTEP
C * * Convert time in min to Julian days.
DAY=(KBND+1)*HALFDT/1440.+1.+DAYOFFSTSWIFT
C SJM: WRITE DAY to screen to monitor sim progression
!WRITE(*,*)DAY !SJM DELETE!
DO L=1,LMAX
IF((L.EQ.LSAL).OR.(L.EQ.LTEMP)) GOTO 1166
IF(DAY.GT.STRCFLOWCONC(L,1)) DAYCHK=STRCFLOWCONC(L,1) !Assumes data
for different L's given at same time in input file
1166
CONTINUE
ENDDO
!10
IF(DAY .GT. STRCFLOWCONC(1))THEN
10
IF(DAY .GT. DAYCHK)THEN
STRCFLOWCONC=STRCFLOWCONC2
!If more than one solute (excl salinity and temp) then need to have
one line in inputfile for each L
!for each day,
!e.g. Line1: Day1 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3)
!
Line2: Day1 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3)
!
Line3: Day2 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3)
!
Line4: Day2 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3)
DO L=1,LMAX
IF(L.EQ.LSAL)GOTO 117 !Skip salinity and temp so don't have to add
these to input file
IF(L.EQ.LTEMP)GOTO 117
READ(IUSFLOWCONCS,*)(STRCFLOWCONC2(L,J), J=1,NUMSTRUCS)
!Assumes
1 solute
DAYCHK=STRCFLOWCONC(L,1)
117
CONTINUE
ENDDO
GO TO 10
ENDIF
RETURN
END
219
Section C2
Important Input Files for the SICS Water-Quality Simulation
Input files and used in the simulation of SICS surface-water phosphorus are
presented. These include the input concentrations at discharge sources
(INPUTFLOWCONCS.dat), the atmospheric deposition data for each of the three
options tested, the SWIFT2D input file (WETLANDS.inp), and the IWQ input file
(IWQINPUT.iwq), which are needed by SWIFT2D. The XML input file (XMLINPUT.xml)
was required for aRSE.
Format for INPUTFLOWCONCS.dat
3
1
90
1
100
1
120
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
16.00
17.00
18.00
19.00
20.00
21.00
22.00
0
90
0
88
0
64
TSB
3
L-31W
3
C-111
3
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0044
0.0101
0.0101
0.0101
0.0101
0.0101
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0062
0.0031
0.0031
0.0031
0.0031
0.0031
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.0032
0.0032
0.0032
0.0032
0.0032
220
23.00
0.0101
24.00
0.0101
25.00
0.0101
26.00
0.0101
27.00
0.0101
28.00
0.0101
29.00
0.0101
30.00
0.0101
*incomplete file
0.0031
0.0031
0.0031
0.0031
0.0031
0.0031
0.0031
0.0031
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
Total Phosphorus Atmospheric Deposition Rates for Model 2
Table C-1 below shows the total phosphorus atmospheric deposition rates applied
to Model 2 for each of the three atmospheric deposition options tested.
Table C-1. Atmospheric deposition rates input to Model 2
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
1
2
3
4
5
6
7
8
9
10
11
12
13
07/15/96
07/16/96
07/17/96
07/18/96
07/19/96
07/20/96
07/21/96
07/22/96
07/23/96
07/24/96
07/25/96
07/26/96
07/27/96
9.93915E-05
0.000686837
3.68857E-05
1.12111E-05
1.38821E-05
0.000110112
1.06841E-06
0
2.1441E-05
4.27002E-06
0
0
2.88908E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
14
15
16
07/28/96
07/29/96
07/30/96
3.36151E-05
0.000136277
1.92605E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
17
18
19
07/31/96
08/1/96
08/2/96
2.67103E-06
2.39848E-05
2.1441E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
20
21
22
23
24
08/3/96
08/4/96
08/5/96
08/6/96
08/7/96
0.000190788
1.33552E-05
2.5075E-05
0.000323431
1.06841E-06
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
221
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
25
26
08/8/96
08/9/96
0.000174071
1.06841E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
27
28
29
08/10/96
08/11/96
08/12/96
6.41411E-06
5.86901E-06
0
9.70874E-05
9.70874E-05
0
8.2192E-05
8.2192E-05
8.2192E-05
30
31
32
08/13/96
08/14/96
08/15/96
2.83457E-05
2.94359E-05
8.64906E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
08/16/96
08/17/96
08/18/96
08/19/96
08/20/96
08/21/96
08/22/96
08/23/96
08/24/96
08/25/96
08/26/96
08/27/96
08/28/96
08/29/96
08/30/96
08/31/96
09/1/96
09/2/96
09/3/96
4.76062E-05
1.76252E-05
0.000174617
0.000723178
0.000256201
0.000159717
0.00018352
0.000261652
4.59709E-05
5.34207E-07
0.000110657
4.90598E-05
1.12111E-05
2.67103E-06
4.48806E-05
9.61209E-06
6.46863E-05
0.000160807
7.37714E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
52
53
54
09/4/96
09/5/96
09/6/96
1.38821E-05
0.000120106
9.61209E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
55
56
57
09/7/96
09/8/96
09/9/96
7.48616E-06
5.92352E-05
0.000437904
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
58
59
60
61
62
63
09/10/96
09/11/96
09/12/96
09/13/96
09/14/96
09/15/96
0.000688654
2.28946E-05
0.000120651
6.41411E-06
0.000113746
1.01572E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
222
Table C-1. Continued
Day
Date
Variable rate
proportionate to rain
volume [g TP/m2/d]
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
64
65
09/16/96
09/17/96
2.56201E-05
0.000174071
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
66
67
68
09/18/96
09/19/96
09/20/96
8.43102E-05
9.50307E-05
0.000325248
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
69
70
71
09/21/96
09/22/96
09/23/96
0.000190788
4.76062E-05
0.000170437
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
09/24/96
09/25/96
09/26/96
09/27/96
09/28/96
09/29/96
09/30/96
10/1/96
10/2/96
10/3/96
10/4/96
10/5/96
10/6/96
10/7/96
10/8/96
10/9/96
10/10/96
10/11/96
10/12/96
6.30509E-05
0
4.27002E-06
0
3.41602E-05
1.54993E-05
0.000368857
6.52314E-05
3.74308E-06
0.000107932
0.000188971
0.000461526
0.000132461
0.000223495
0.000236214
0.000130826
0
0
0.001019354
9.70874E-05
0
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
91
92
93
10/13/96
10/14/96
10/15/96
0.001010269
0.000228946
0.000288908
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
94
95
96
10/16/96
10/17/96
10/18/96
6.46863E-05
0.000423368
0.000310712
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
97
98
99
100
101
102
10/19/96
10/20/96
10/21/96
10/22/96
10/23/96
10/24/96
8.70357E-05
3.19797E-06
1.60262E-06
1.60262E-06
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
223
Table C-1. Continued
Day
Date
Variable rate
proportionate to rain
volume [g TP/m2/d]
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
103
104
10/25/96
10/26/96
3.74308E-06
1.06841E-06
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
105
106
107
10/27/96
10/28/96
10/29/96
8.54004E-06
1.06841E-06
0
9.70874E-05
9.70874E-05
0
8.2192E-05
8.2192E-05
8.2192E-05
108
109
110
10/30/96
10/31/96
11/1/96
1.70982E-05
5.34207E-07
5.34207E-07
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
11/2/96
11/3/96
11/4/96
11/5/96
11/6/96
11/7/96
11/8/96
11/9/96
11/10/96
11/11/96
11/12/96
11/13/96
11/14/96
11/15/96
11/16/96
11/17/96
11/18/96
11/19/96
11/20/96
3.74308E-06
5.34207E-07
2.1441E-06
1.81703E-05
0
3.74308E-06
1.06841E-06
0
0
0
0
0
5.015E-05
4.59709E-05
1.54993E-05
0
2.1441E-06
1.06841E-06
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
130
131
132
11/21/96
11/22/96
11/23/96
1.06841E-06
2.67103E-06
4.81513E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
133
134
135
11/24/96
11/25/96
11/26/96
0
0
0
0
0
0
8.2192E-05
8.2192E-05
8.2192E-05
136
137
138
139
140
141
11/27/96
11/28/96
11/29/96
11/30/96
12/1/96
12/2/96
0
7.21361E-05
0
0
0
1.33552E-05
0
9.70874E-05
0
0
0
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
224
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
142
143
12/3/96
12/4/96
1.12111E-05
0
9.70874E-05
0
8.2192E-05
8.2192E-05
144
145
146
12/5/96
12/6/96
12/7/96
7.63152E-05
1.33552E-05
5.34207E-07
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
147
148
149
12/8/96
12/9/96
12/10/96
4.81513E-06
0
0
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
12/11/96
12/12/96
12/13/96
12/14/96
12/15/96
12/16/96
12/17/96
12/18/96
12/19/96
12/20/96
12/21/96
12/22/96
12/23/96
12/24/96
12/25/96
12/26/96
12/27/96
12/28/96
12/29/96
0
0
0.000261652
4.27002E-06
1.06841E-06
0
0
8.54004E-06
4.81513E-06
0
5.34207E-07
6.41411E-06
0
0
1.06841E-06
8.54004E-06
4.81513E-06
1.06841E-06
2.67103E-06
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
169
170
171
12/30/96
12/31/96
01/1/97
4.81513E-06
1.06841E-06
1.06841E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
172
173
174
01/2/97
01/3/97
01/4/97
1.60262E-06
1.06841E-06
2.1441E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
175
176
177
178
179
180
01/5/97
01/6/97
01/7/97
01/8/97
01/9/97
01/10/97
5.34207E-07
1.06841E-06
6.41411E-06
4.81513E-06
1.60262E-06
9.72111E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
225
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
181
182
01/11/97
01/12/97
1.60262E-05
0.000359772
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
183
184
185
01/13/97
01/14/97
01/15/97
0.000370674
0.000168802
0.000185337
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
186
187
188
01/16/97
01/17/97
01/18/97
0.00020169
0
0
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
01/19/97
01/20/97
01/21/97
01/22/97
01/23/97
01/24/97
01/25/97
01/26/97
01/27/97
01/28/97
01/29/97
01/30/97
01/31/97
02/1/97
02/2/97
02/3/97
02/4/97
02/5/97
02/6/97
0
0
5.34207E-07
1.06841E-06
5.34207E-07
0
3.74308E-05
3.90661E-05
0
1.44272E-05
0.000134097
8.34017E-05
0
0
2.1441E-06
3.19797E-06
2.39848E-05
4.81513E-06
1.60262E-06
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
208
209
210
02/7/97
02/8/97
02/9/97
5.34207E-07
2.1441E-06
1.65531E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
211
212
213
02/10/97
02/11/97
02/12/97
1.06841E-06
0
0
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
214
215
216
217
218
219
02/13/97
02/14/97
02/15/97
02/16/97
02/17/97
02/18/97
5.34207E-07
6.41411E-06
1.06841E-06
0.000152267
9.61209E-06
0.00020169
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
226
Table C-1. Continued
Day
Date
Variable rate
proportionate to rain
volume [g TP/m2/d]
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
220
221
02/19/97
02/20/97
2.39848E-05
3.74308E-06
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
222
223
224
02/21/97
02/22/97
02/23/97
5.34207E-07
5.34207E-07
2.1441E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
225
226
227
02/24/97
02/25/97
02/26/97
2.72554E-05
1.60262E-05
0
9.70874E-05
9.70874E-05
0
8.2192E-05
8.2192E-05
8.2192E-05
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
02/27/97
02/28/97
03/1/97
03/2/97
03/3/97
03/4/97
03/5/97
03/6/97
03/7/97
03/8/97
03/9/97
03/10/97
03/11/97
03/12/97
03/13/97
03/14/97
03/15/97
03/16/97
03/17/97
0
0
0
0
5.34207E-07
5.34207E-07
0
4.27002E-06
1.33552E-05
5.34207E-07
5.34207E-07
5.86901E-06
5.34207E-07
2.1441E-06
5.34207E-07
0.000632326
8.23114E-05
1.06841E-06
5.34207E-07
0
0
0
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
247
248
249
03/18/97
03/19/97
03/20/97
0
1.06841E-06
5.34207E-07
0
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
250
251
252
03/21/97
03/22/97
03/23/97
0.000219861
6.41411E-06
5.34207E-07
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
253
254
255
256
257
258
03/24/97
03/25/97
03/26/97
03/27/97
03/28/97
03/29/97
0.000106296
1.28282E-05
0
1.81703E-05
2.67103E-06
5.34207E-07
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
227
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
259
260
03/30/97
03/31/97
5.34207E-07
2.08958E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
261
262
263
04/1/97
04/2/97
04/3/97
2.1441E-06
0
0
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
264
265
266
04/4/97
04/5/97
04/6/97
0
0
0
0
0
0
8.2192E-05
8.2192E-05
8.2192E-05
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
04/7/97
04/8/97
04/9/97
04/10/97
04/11/97
04/12/97
04/13/97
04/14/97
04/15/97
04/16/97
04/17/97
04/18/97
04/19/97
04/20/97
04/21/97
04/22/97
04/23/97
04/24/97
04/25/97
0
2.1441E-06
3.14346E-05
1.44272E-05
1.70982E-05
5.39658E-05
7.10459E-05
3.19797E-06
0.000117562
0.000141002
1.01572E-05
0
0
0
1.92605E-05
9.08515E-06
5.86901E-06
4.27002E-06
3.19797E-06
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
286
287
288
04/26/97
04/27/97
04/28/97
0.000129191
2.67103E-06
0.000134097
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
289
290
291
04/29/97
04/30/97
05/1/97
1.33552E-05
9.55758E-05
5.86901E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
292
293
294
295
296
297
05/2/97
05/3/97
05/4/97
05/5/97
05/6/97
05/7/97
6.94105E-06
0
6.30509E-05
1.01572E-05
0
0
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
228
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
298
299
05/8/97
05/9/97
0
0
0
0
8.2192E-05
8.2192E-05
300
301
302
05/10/97
05/11/97
05/12/97
0
1.06841E-06
0.000466977
0
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
303
304
305
05/13/97
05/14/97
05/15/97
0.000145362
0
5.34207E-07
9.70874E-05
0
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
05/16/97
05/17/97
05/18/97
05/19/97
05/20/97
05/21/97
05/22/97
05/23/97
05/24/97
05/25/97
05/26/97
05/27/97
05/28/97
05/29/97
05/30/97
05/31/97
06/1/97
06/2/97
06/3/97
0
2.08958E-05
6.41411E-06
2.1441E-06
5.34207E-06
1.60262E-05
0.000181158
8.81259E-05
0.000179523
0
4.54257E-05
5.34207E-07
0.000259835
0.000100482
7.05008E-05
0.000119197
0.000122831
0.000739531
7.26812E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
325
326
327
06/4/97
06/5/97
06/6/97
1.70982E-05
4.81513E-06
0
9.70874E-05
9.70874E-05
0
8.2192E-05
8.2192E-05
8.2192E-05
328
329
330
06/7/97
06/8/97
06/9/97
1.17562E-05
0.000741348
0.004197339
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
331
332
333
334
335
336
06/10/97
06/11/97
06/12/97
06/13/97
06/14/97
06/15/97
0.001475428
0.000292542
1.92605E-05
2.88908E-05
1.38821E-05
0.000432453
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
229
Table C-1. Continued
Day
Date
Variable rate
proportionate to rain
volume [g TP/m2/d]
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
337
338
06/16/97
06/17/97
0.000115926
2.1441E-06
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
339
340
341
06/18/97
06/19/97
06/20/97
3.19797E-06
4.27002E-06
1.54993E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
342
343
344
06/21/97
06/22/97
06/23/97
7.57701E-05
0.000414283
7.05008E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
06/24/97
06/25/97
06/26/97
06/27/97
06/28/97
06/29/97
06/30/97
07/1/97
07/2/97
07/3/97
07/4/97
07/5/97
07/6/97
07/7/97
07/8/97
07/9/97
07/10/97
07/11/97
07/12/97
0.000185337
0.000101027
9.08515E-06
1.17562E-05
0
1.60262E-06
5.77815E-05
0.000135732
0.000247116
9.88464E-05
0.000321614
4.27002E-06
3.36151E-05
5.86901E-06
5.86901E-06
4.27002E-06
0.000108477
0.000144272
0.000254384
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
364
365
366
07/13/97
07/14/97
07/15/97
0.000205324
0.000185337
5.34207E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
367
368
369
07/16/97
07/17/97
07/18/97
0.000243482
0.000161897
0.000156446
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
370
371
372
373
374
375
07/19/97
07/20/97
07/21/97
07/22/97
07/23/97
07/24/97
0.000142092
0.000118107
3.47053E-05
0.00020169
0.000120651
1.06841E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
230
Table C-1. Continued
Day
Date
Variable rate
proportionate to rain
volume [g TP/m2/d]
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
376
377
07/25/97
07/26/97
9.61209E-06
0.000123376
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
378
379
380
07/27/97
07/28/97
07/29/97
5.77815E-05
2.1441E-05
5.34207E-07
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
381
382
383
07/30/97
07/31/97
08/1/97
4.27002E-06
1.81703E-05
0.000160262
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
08/2/97
08/3/97
08/4/97
08/5/97
08/6/97
08/7/97
08/8/97
08/9/97
08/10/97
08/11/97
08/12/97
08/13/97
08/14/97
08/15/97
08/16/97
08/17/97
08/18/97
08/19/97
08/20/97
0.000107386
0
7.63152E-05
7.48616E-06
0.000110657
4.161E-05
5.45109E-05
0.000354321
0.00021441
3.96112E-05
2.78006E-05
0
5.34207E-07
0.000153357
3.99747E-05
6.41411E-06
1.60262E-05
5.86901E-06
7.37714E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
403
404
405
08/21/97
08/22/97
08/23/97
0.000252567
2.5075E-05
2.19861E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
406
407
408
08/24/97
08/25/97
08/26/97
4.70611E-05
0.000199873
0.000121741
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
409
410
411
412
413
414
08/27/97
08/28/97
08/29/97
08/30/97
08/31/97
09/1/97
0.000128282
4.81513E-05
6.72301E-05
0.000279823
0.000219861
0.000138276
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
231
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain
day [g TP/m2/d]
Constant rate per day
[g TP/m2/d]
415
416
09/2/97
09/3/97
0.000133552
3.25248E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
417
418
419
09/4/97
09/5/97
09/6/97
9.83013E-05
0.000321614
0.000305261
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
420
421
422
09/7/97
09/8/97
09/9/97
4.27002E-06
3.47053E-05
1.06841E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
09/10/97
09/11/97
09/12/97
09/13/97
09/14/97
09/15/97
09/16/97
09/17/97
09/18/97
09/19/97
09/20/97
09/21/97
09/22/97
09/23/97
09/24/97
09/25/97
09/26/97
09/27/97
09/28/97
5.34207E-07
9.24868E-05
5.72364E-05
4.43355E-05
0.000100482
0.000129191
3.52504E-05
0.000116472
5.86901E-05
0.000198056
3.30699E-05
2.34397E-05
2.1441E-06
3.41602E-05
0.000119742
5.72364E-05
0.000221678
6.03254E-05
0.000207141
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
442
443
444
09/29/97
09/30/97
10/1/97
0.000223495
0.000332516
0.000288908
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
445
446
447
10/2/97
10/3/97
10/4/97
0.000187154
4.81513E-06
2.1441E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
448
449
450
451
452
453
10/5/97
10/6/97
10/7/97
10/8/97
10/9/97
10/10/97
4.81513E-06
9.55758E-05
2.1441E-06
0
4.81513E-06
0.000104116
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
232
Table C-1. Continued
Day
Variable rate
proportionate to rain
volume [g TP/m2/d]
Date
Constant rate per rain day Constant rate per day
[g TP/m2/d]
[g TP/m2/d]
454
455
10/11/97
10/12/97
6.94105E-06
2.5075E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
456
457
458
10/13/97
10/14/97
10/15/97
9.61209E-06
7.48616E-06
2.67103E-06
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
459
460
461
10/16/97
10/17/97
10/18/97
1.28282E-05
9.08515E-06
1.22831E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
10/19/97
10/20/97
10/21/97
10/22/97
10/23/97
10/24/97
10/25/97
10/26/97
10/27/97
10/28/97
10/29/97
10/30/97
10/31/97
11/1/97
11/2/97
11/3/97
11/4/97
11/5/97
11/6/97
0
1.06841E-05
0
0
5.34207E-07
0
5.34207E-07
5.34207E-07
0
0
1.01572E-05
0.000236214
2.1441E-06
0
9.61209E-06
5.72364E-05
2.1441E-06
1.01572E-05
4.81513E-06
0
9.70874E-05
0
0
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
481
482
483
11/7/97
11/8/97
11/9/97
3.74308E-06
0
0
9.70874E-05
0
0
8.2192E-05
8.2192E-05
8.2192E-05
484
485
486
11/10/97
11/11/97
11/12/97
0
1.06841E-06
0
0
9.70874E-05
0
8.2192E-05
8.2192E-05
8.2192E-05
233
Section C3
XML Input File for Model 3 (XMLINPUT.xml)
<?xml version="1.0" encoding="utf-8"?>
<wq version="0.1">
<reaction_sets>
<reaction_set name="rs1" full_name="Reaction Set Number 1">
<coverage>
<cell>all</cell>
<segment>all</segment>
</coverage>
<stores>
<store full_name="Surface-water" distribution="heterogeneous"
location="element" section="gw" actuator="rsm_wm">
<name>surface_water</name>
<components>
<variables>
<variable type="mobile">
<name full_name="Water Column TP">Sal</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="mobile">
<name full_name="Water Column TP">TP_sw_conc</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_sw_mass1</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_sw_mass2</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_uptake1</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_uptake2</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
234
<name full_name="Water Column TP">TP_soil1</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_soil2</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_live1</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_live2</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_dead1</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_dead2</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_senesc</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_decomp</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">TP_bury</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</variable>
<variable type="stabile">
<name full_name="Water Column TP">K_wet</name>
<initial_distribution type="constant">
235
10.0
</initial_distribution>
</variable>
</variables>
<parameters>
<parameter units="meter">
<name>longitudinal_dispersivity</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</parameter>
<parameter units="meter">
<name>transverse_dispersivity</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</parameter>
<parameter units="meter">
<name>molecular_diffusion</name>
<initial_distribution type="constant">
0.00001
</initial_distribution>
</parameter>
<parameter units="none">
<name>surface_porosity</name>
<initial_distribution type="constant">
1.0
</initial_distribution>
</parameter>
<parameter units="meter">
<name>subsurface_longitudinal_dispersivity</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</parameter>
<parameter units="meter">
<name>subsurface_transverse_dispersivity</name>
<initial_distribution type="constant">
10.0
</initial_distribution>
</parameter>
<parameter units="meter">
<name>subsurface_molecular_diffusion</name>
<initial_distribution type="constant">
0.00001
</initial_distribution>
</parameter>
<parameter units="none">
<name>subsurface_porosity</name>
<initial_distribution type="constant">
1.0
</initial_distribution>
</parameter>
<parameter units="none">
<name>k_uptake</name>
<initial_distribution type="constant">
236
0.084375
</initial_distribution>
</parameter>
<parameter units="none">
<name>k_senesc</name>
<initial_distribution type="constant">
0.25
</initial_distribution>
</parameter>
<parameter units="none">
<name>k_decomp</name>
<initial_distribution type="constant">
0.0001
</initial_distribution>
</parameter>
<parameter units="none">
<name>k_soil</name>
<initial_distribution type="constant">
0.13
</initial_distribution>
</parameter>
</parameters>
</components>
</store>
</stores>
<equations>
<equation type="pre">
<lhs>TP_sw_mass2</lhs>
<rhs>(1-k_uptake)*TP_sw_conc*depth</rhs>
</equation>
<equation type="pre">
<lhs>TP_uptake2</lhs>
<rhs>k_uptake*K_wet*TP_sw_mass1</rhs>
</equation>
<equation type="pre">
<lhs>TP_senesc</lhs>
<rhs>k_senesc*TP_uptake1</rhs>
</equation>
<equation type="pre">
<lhs>TP_decomp</lhs>
<rhs>k_decomp*TP_dead2</rhs>
</equation>
<equation type="pre">
<lhs>TP_bury</lhs>
<rhs>k_soil*TP_uptake1</rhs>
</equation>
<equation type="pre">
<lhs>TP_live1</lhs>
<rhs>TP_live2</rhs>
</equation>
<equation type="pre">
<lhs>TP_dead1</lhs>
<rhs>TP_dead2</rhs>
</equation>
<equation type="pre">
<lhs>TP_soil1</lhs>
237
<rhs>TP_soil2</rhs>
</equation>
<equation type="post">
<lhs>TP_uptake1</lhs>
<rhs>TP_uptake2</rhs>
</equation>
<equation type="post">
<lhs>TP_sw_mass1</lhs>
<rhs>TP_sw_mass2</rhs>
</equation>
<equation type="post">
<lhs>TP_dead2</lhs>
<rhs>TP_dead1+TP_senesc-TP_decomp</rhs>
</equation>
<equation type="post">
<lhs>TP_live2</lhs>
<rhs>TP_live1+TP_uptake2-TP_senesc</rhs>
</equation>
<equation type="post">
<lhs>TP_soil2</lhs>
<rhs>TP_soil1+TP_bury</rhs>
</equation>
<equation type="post">
<lhs>TP_sw_conc</lhs>
<rhs>(TP_sw_mass2+TP_decomp)/depth</rhs>
</equation>
</equations>
</reaction_set>
</reaction_sets>
</wq>
IWQ input File for Model 3 (IWQINPUT.iwq)
1 2 14 5 1 0
'XMLINPUT.xml' 'XMLOUTPUT.xml' 'rs1'
Sal 5.01 TP_sw_conc 0.005
TP_sw_mass1 0.01 TP_sw_mass2 0.01 TP_uptake1 0.0008 TP_uptake2 0.0008
TP_soil1 0.0001 TP_soil2 0.0001 TP_live1 0.04 TP_live2 0.04 TP_dead1 0.014
TP_dead2 0.014 TP_senesc 0.0002 TP_decomp 0.0001 TP_bury 0 K_wet 1
00000000000000
k_uptake 0.084375 k_senesc 0.25 k_decomp 0.0001 k_soil 0.0
0
depth 0.52 time_step 3600 area 92903
238
SWIFT2D Input File (WETLANDS.inp) for Model 3
SOUTHERN INLAND AND COASTAL SYSTEMS MODEL
END NOTE
END NOTE
NOSAMV=
1(NUMBER OF DIMENSIONS THAT MUST STAY THE SAME)
NODIMV=
2(NUMBER OF DIMENSIONS TOTAL)
WETMTZ /IDP...R07
00
00
00
00
00
RUN NUMBER 1
R2 TITL
WETLANDS
15 JUL '96 98/ 8/2517:23:39 IDPV514
R3 DATE
Halfdt Titide Tstart Trst Tstop Tirst Tihisp Tihist DAYOFFSTSWIFT
1.50 15.0 0.0 0.0 999999. 999999. 1440. 1440.
0 R4 TIMEA
99999999999999999999999. 45. 30.999999 60.999999999999999999 0.R5 TIMEB
0 0 2 1 0 5 1 0 0 0 0 0R6 FLAGS
7 3 4 4 0 4
R7 INPR1
1
R8 INPR2
0 1440 1440 1440 0 0 0 0 0
R9 OTPR1
1440 1440 1440 1440 0 0 0
R10OTPR2
545760545880546000546120546240546360546480546600546720546840546960547080R11 PRT1
547200547320547440547560547680547800547920548040548160548280548400548520R12 PRT2
548640548760548880549000549120549240549360549480549600549720549840549960R13 PRT3
550080550200550320550440550560550680
148 98 2 14 33 4 25 3 5 8 0 1R15 DIMA
94 128
R16 DIMB
0.5 0
1
R17 CNST
25.000 0.0 304.8 0.20 0.0 0.10 1. 1.00 0.5 1.0 5.0 300.0R18 PHCH
9.81 0.0012 1.205 998.2 1.0000 14.3 1000.0 0.97 0.0023R19 COFA
FR80
35SPRO
1.0 1.0
R20 Ploter D
25 1 0.0 13.0 20.0 14.0K/HR
5
R21 Nctitl D
4.0 170.0 2.00 121.0 163.0 1.25 74.0 89.0 1.00 122.0 103.0 1.00R22 Hx USED
1.0 2.0 2.0 2.0 2.0
R23 Dxpdy ED
1 1 2 0.5 1.0 -0.40 -0.40 0.25 1.0 0.0 1 1R24Iplc SED
R25 Linx SED
25.0 1.0250 0.698 1.0
R26 COFB
1 57 36 CP
RS1 WL-Sta
2 109 78 EVER4
RS1 WL-Sta
3 100 58 EVER5A
RS1 WL-Sta
4 69 45 E146
RS1 WL-Sta
5 98 97 E158
RS1 WL-Sta
6 142 52 EP12R
RS1 WL-Sta
7 139 57 EP1R
RS1 WL-Sta
8 123 55 EPGW
RS1 WL-Sta
9 120 61 EVER6
RS1 WL-Sta
10 110 65 EVER7
RS1 WL-Sta
11 74 73 NP67
RS1 WL-Sta
12 62 56 P37
RS1 WL-Sta
13 89 81 R127
RS1 WL-Sta
14 81 66 TSH
RS1 WL-Sta
1 28 18 Alligat_T
RS2 Curr-Sta
2 28 17 Alligat_C
RS2 Curr-Sta
3 28 16 Alligat_B
RS2 Curr-Sta
4 47 14 McCorm_L
RS2 Curr-Sta
5 48 14 McCorm_C
RS2 Curr-Sta
6 49 14 McCorm_R
RS2 Curr-Sta
7 77 23 Taylor_L
RS2 Curr-Sta
8 78 23 Taylor_C
RS2 Curr-Sta
9 79 23 Taylor_R
RS2 Curr-Sta
10 84 26 East_L
RS2 Curr-Sta
11 85 26 East_C
RS2 Curr-Sta
12 86 26 East_R
RS2 Curr-Sta
13 96 27 Mud_T
RS2 Curr-Sta
14 96 28 Mud_C
RS2 Curr-Sta
15 96 29 Mud_B
RS2 Curr-Sta
16 113 32 Trout_L
RS2 Curr-Sta
17 114 32 Trout_C
RS2 Curr-Sta
18 115 32 Trout_R
RS2 Curr-Sta
19 127 30 Shell_L
RS2 Curr-Sta
20 128 30 Shell_C
RS2 Curr-Sta
21 129 30 Shell_R
RS2 Curr-Sta
22 128 36 Stillw_L
RS2 Curr-Sta
239
R14 PRT4
23 129 36 Stillw_C
24 130 36 Stillw_R
25 138 40 Oregon_L
26 139 40 Oregon_C
27 140 40 Oregon_R
28 140 41 WestHi_L
29 141 41 WestHi_C
30 142 41 WestHi_R
31 142 42 EastHi_L
32 143 42 EastHi_C
33 144 42 EastHi_R
1 90 90 TSB
2 100 88 L-31W
3 120 64 C-111
4 148 98 Dummy (ex solar)
1 57 36 CP
2 109 78 EVER4
3 100 58 EVER5A
4 69 45 E146
5 98 97 E158
6 142 52 EP12R
7 139 57 EP1R
8 123 55 EPGW
9 120 61 EVER6
10 110 65 EVER7
11 74 73 NP67
12 62 56 P37
13 89 81 R127
14 81 66 TSH
15 28 17 Alligat_c
16 48 14 McCorm_c
17 78 23 Taylor_c
18 85 26 East_c
19 96 28 Mud_c
20 114 32 Trout_c
21 128 30 Shell_c
22 129 36 Stillw_c
23 139 40 Oregon_c
24 141 41 WestHi_c
25 143 42 EastHi_c
1 93 31 36 Joe Bay 1
2 98 36 40 Joe Bay 2
3 116 34 39 Joe Bay 3
1 36 93 98 Joe Bay 4
2 40 98 101 Joe Bay 5
3 41 102 107 Joe Bay 6
4 40 108 110 Joe Bay 7
5 39 111 116 Joe Bay 8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
13
15
17
18
19
19
20
20
20
21
23
26
27
27
28
28
28
30
31
32
17
16
15
14
17
18
15
16
19
20
21
19
18
15
17
16
14
14
13
15
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS3 Src
RS3 Src
RS3 Src
RS3 Sol
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS5 U-tran-Sta
RS5 U-tran-Sta
RS5 U-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS7 Dam
RS8 Wind/Temp
RS9 Bar/Sluice
Alligator
240
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
33
35
36
38
40
41
42
42
43
44
46
46
47
49
50
50
51
52
54
56
57
58
58
59
60
61
63
64
66
68
69
69
70
70
70
71
71
71
71
73
74
74
76
78
80
81
83
84
86
89
91
92
94
96
96
96
98
100
102
104
105
107
109
111
113
114
115
116
118
119
13
12
13
13
12
11
12
13
14
13
13
18
14
14
16
17
12
11
10
9
10
11
12
13
14
15
16
17
17
17
16
15
14
18
19
15
16
17
20
21
22
23
23
23
24
25
25
26
26
27
27
26
26
27
28
29
30
30
30
30
31
31
30
31
31
32
33
34
34
33
Mud Creek
241
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
91
92
93
94
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
120 32
121 31
122 30
123 29
4 18
5 18
6 18
7 18
8 18
9 18
10 18
11 17
12 17
13 17
14 16
15 16
16 15
17 15
18 14
19 15
20 19
21 20
22 21
23 21
24 20
25 20
25 25
26 19
27 15
27 18
28 14
29 14
29 25
30 14
31 13
32 13
33 13
34 12
34 20
35 12
36 13
37 13
38 13
39 12
40 12
41 11
43 14
44 13
45 13
46 13
48 14
49 14
50 16
51 12
52 11
53 10
54 10
55 9
56 9
57 10
59 13
60 14
61 15
62 16
63 16
64 17
65 17
66 17
67 17
68 17
McCormick Creek
242
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
67 70 14
68 71 20
69 72 21
70 73 21
71 75 23
72 76 23
73 77 23
74 78 23
Taylor Creek
75 79 23
76 80 24
77 81 25
78 82 25
79 83 25
80 84 26
81 85 26
East Creek
82 86 26
83 87 26
84 88 27
85 89 27
86 90 27
87 91 27
88 92 26
89 93 26
90 94 26
91 95 26
92 97 30
93 98 30
94 99 30
95 100 30
96 101 30
97 102 30
98 103 30
99 104 30
100 105 31
101 106 31
102 107 31
103 108 31
104 109 30
105 110 30
106 111 31
107 112 31
108 113 31
109 114 32
Trout Creek
110 115 33
111 116 34
112 117 34
113 118 34
114 119 33
115 120 32
116 121 31
117 122 30
118 123 29
119 127 29
120 128 30
Shell Creek
121 129 36
Stillwater Creek
122 130 36
123 138 40
124 139 40
Oregon Creek
125 140 41
126 141 41
West Highway
127 142 42
128 143 42
East Highway
1269.9778269.9778269.9778269.9778269.9778269.9778
2269.9778269.9778269.9778269.9778269.9778269.9778
3269.9778269.9778269.9778269.9778269.9778269.9778
4269.9778269.9778269.9778269.9778269.9778269.9778
5269.9778269.9778269.9778269.9778269.9778269.9778
6269.9778269.9778269.9778269.9778269.9778269.9778
7269.9778269.9778269.9778269.9778269.9778269.9778
8 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
243
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9269.9778269.9778269.9778269.9778269.9778269.9778
10269.9778269.9778269.9778269.9778269.9778269.9778
11269.9778269.9778269.9778269.9778269.9778269.9778
12269.9778269.9778269.9778269.9778269.9778269.9778
13269.9778269.9778269.9778269.9778269.9778269.9778
14269.9778269.9778269.9778269.9778269.9778269.9778
15 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978
16269.9778269.9778269.9778269.9778269.9778269.9778
17269.9778269.9778269.9778269.9778269.9778269.9778
18269.9778269.9778269.9778269.9778269.9778269.9778
19269.9778269.9778269.9778269.9778269.9778269.9778
20 53.9956 53.9956 53.9956 53.9956 53.9956 53.9956
21269.9778269.9778269.9778269.9778269.9778269.9778
22269.9778269.9778269.9778269.9778269.9778269.9778
23269.9778269.9778269.9778269.9778269.9778269.9778
24269.9778269.9778269.9778269.9778269.9778269.9778
25269.9778269.9778269.9778269.9778269.9778269.9778
26269.9778269.9778269.9778269.9778269.9778269.9778
27269.9778269.9778269.9778269.9778269.9778269.9778
28269.9778269.9778269.9778269.9778269.9778269.9778
29269.9778269.9778269.9778269.9778269.9778269.9778
30269.9778269.9778269.9778269.9778269.9778269.9778
31269.9778269.9778269.9778269.9778269.9778269.9778
32 32.3973 32.3973 32.3973 32.3973 32.3973 32.3973
33269.9778269.9778269.9778269.9778269.9778269.9778
34269.9778269.9778269.9778269.9778269.9778269.9778
35 21.5982 21.5982 21.5982 21.5982 21.5982 21.5982
36269.9778269.9778269.9778269.9778269.9778269.9778
37269.9778269.9778269.9778269.9778269.9778269.9778
38269.9778269.9778269.9778269.9778269.9778269.9778
39269.9778269.9778269.9778269.9778269.9778269.9778
40269.9778269.9778269.9778269.9778269.9778269.9778
41269.9778269.9778269.9778269.9778269.9778269.9778
42269.9778269.9778269.9778269.9778269.9778269.9778
43269.9778269.9778269.9778269.9778269.9778269.9778
44269.9778269.9778269.9778269.9778269.9778269.9778
45269.9778269.9778269.9778269.9778269.9778269.9778
46269.9778269.9778269.9778269.9778269.9778269.9778
47269.9778269.9778269.9778269.9778269.9778269.9778
48 32.3973 32.3973 32.3973 32.3973 32.3973 32.3973
49269.9778269.9778269.9778269.9778269.9778269.9778
50269.9778269.9778269.9778269.9778269.9778269.9778
51269.9778269.9778269.9778269.9778269.9778269.9778
52269.9778269.9778269.9778269.9778269.9778269.9778
53269.9778269.9778269.9778269.9778269.9778269.9778
54269.9778269.9778269.9778269.9778269.9778269.9778
55269.9778269.9778269.9778269.9778269.9778269.9778
56269.9778269.9778269.9778269.9778269.9778269.9778
57269.9778269.9778269.9778269.9778269.9778269.9778
58269.9778269.9778269.9778269.9778269.9778269.9778
59269.9778269.9778269.9778269.9778269.9778269.9778
60269.9778269.9778269.9778269.9778269.9778269.9778
61269.9778269.9778269.9778269.9778269.9778269.9778
62269.9778269.9778269.9778269.9778269.9778269.9778
63269.9778269.9778269.9778269.9778269.9778269.9778
64269.9778269.9778269.9778269.9778269.9778269.9778
65269.9778269.9778269.9778269.9778269.9778269.9778
66269.9778269.9778269.9778269.9778269.9778269.9778
67269.9778269.9778269.9778269.9778269.9778269.9778
68269.9778269.9778269.9778269.9778269.9778269.9778
69269.9778269.9778269.9778269.9778269.9778269.9778
70269.9778269.9778269.9778269.9778269.9778269.9778
71269.9778269.9778269.9778269.9778269.9778269.9778
72269.9778269.9778269.9778269.9778269.9778269.9778
73269.9778269.9778269.9778269.9778269.9778269.9778
74269.9778269.9778269.9778269.9778269.9778269.9778
75 18.8984 18.8984 18.8984 18.8984 18.8984 18.8984
76269.9778269.9778269.9778269.9778269.9778269.9778
77269.9778269.9778269.9778269.9778269.9778269.9778
78269.9778269.9778269.9778269.9778269.9778269.9778
244
Alligator
Mud Creek
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
79269.9778269.9778269.9778269.9778269.9778269.9778
80269.9778269.9778269.9778269.9778269.9778269.9778
81269.9778269.9778269.9778269.9778269.9778269.9778
82269.9778269.9778269.9778269.9778269.9778269.9778
83269.9778269.9778269.9778269.9778269.9778269.9778
84269.9778269.9778269.9778269.9778269.9778269.9778
85269.9778269.9778269.9778269.9778269.9778269.9778
86269.9778269.9778269.9778269.9778269.9778269.9778
87269.9778269.9778269.9778269.9778269.9778269.9778
88269.9778269.9778269.9778269.9778269.9778269.9778
89269.9778269.9778269.9778269.9778269.9778269.9778
90269.9778269.9778269.9778269.9778269.9778269.9778
91269.9778269.9778269.9778269.9778269.9778269.9778
92269.9778269.9778269.9778269.9778269.9778269.9778
93269.9778269.9778269.9778269.9778269.9778269.9778
94269.9778269.9778269.9778269.9778269.9778269.9778
1269.9778269.9778269.9778269.9778269.9778269.9778
2269.9778269.9778269.9778269.9778269.9778269.9778
3269.9778269.9778269.9778269.9778269.9778269.9778
4269.9778269.9778269.9778269.9778269.9778269.9778
5269.9778269.9778269.9778269.9778269.9778269.9778
6269.9778269.9778269.9778269.9778269.9778269.9778
7269.9778269.9778269.9778269.9778269.9778269.9778
8269.9778269.9778269.9778269.9778269.9778269.9778
9269.9778269.9778269.9778269.9778269.9778269.9778
10269.9778269.9778269.9778269.9778269.9778269.9778
11269.9778269.9778269.9778269.9778269.9778269.9778
12269.9778269.9778269.9778269.9778269.9778269.9778
13269.9778269.9778269.9778269.9778269.9778269.9778
14269.9778269.9778269.9778269.9778269.9778269.9778
15269.9778269.9778269.9778269.9778269.9778269.9778
16269.9778269.9778269.9778269.9778269.9778269.9778
17269.9778269.9778269.9778269.9778269.9778269.9778
18269.9778269.9778269.9778269.9778269.9778269.9778
19269.9778269.9778269.9778269.9778269.9778269.9778
20269.9778269.9778269.9778269.9778269.9778269.9778
21269.9778269.9778269.9778269.9778269.9778269.9778
22269.9778269.9778269.9778269.9778269.9778269.9778
23 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
24269.9778269.9778269.9778269.9778269.9778269.9778
25269.9778269.9778269.9778269.9778269.9778269.9778
26269.9778269.9778269.9778269.9778269.9778269.9778
27269.9778269.9778269.9778269.9778269.9778269.9778
28269.9778269.9778269.9778269.9778269.9778269.9778
29 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
30269.9778269.9778269.9778269.9778269.9778269.9778
31269.9778269.9778269.9778269.9778269.9778269.9778
32269.9778269.9778269.9778269.9778269.9778269.9778
33269.9778269.9778269.9778269.9778269.9778269.9778
34269.9778269.9778269.9778269.9778269.9778269.9778
35 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
36269.9778269.9778269.9778269.9778269.9778269.9778
37269.9778269.9778269.9778269.9778269.9778269.9778
38269.9778269.9778269.9778269.9778269.9778269.9778
39269.9778269.9778269.9778269.9778269.9778269.9778
40269.9778269.9778269.9778269.9778269.9778269.9778
41269.9778269.9778269.9778269.9778269.9778269.9778
42269.9778269.9778269.9778269.9778269.9778269.9778
43269.9778269.9778269.9778269.9778269.9778269.9778
44269.9778269.9778269.9778269.9778269.9778269.9778
45269.9778269.9778269.9778269.9778269.9778269.9778
46269.9778269.9778269.9778269.9778269.9778269.9778
47 37.1219 37.1219 37.1219 37.1219 37.1219 37.1219
48269.9778269.9778269.9778269.9778269.9778269.9778
49269.9778269.9778269.9778269.9778269.9778269.9778
50269.9778269.9778269.9778269.9778269.9778269.9778
51269.9778269.9778269.9778269.9778269.9778269.9778
52 18.8984 18.8984 18.8984 18.8984 18.8984 18.8984
53269.9778269.9778269.9778269.9778269.9778269.9778
54269.9778269.9778269.9778269.9778269.9778269.9778
245
McCormick Creek
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
55269.9778269.9778269.9778269.9778269.9778269.9778
56269.9778269.9778269.9778269.9778269.9778269.9778
57269.9778269.9778269.9778269.9778269.9778269.9778
58269.9778269.9778269.9778269.9778269.9778269.9778
59269.9778269.9778269.9778269.9778269.9778269.9778
60269.9778269.9778269.9778269.9778269.9778269.9778
61269.9778269.9778269.9778269.9778269.9778269.9778
62269.9778269.9778269.9778269.9778269.9778269.9778
63269.9778269.9778269.9778269.9778269.9778269.9778
64269.9778269.9778269.9778269.9778269.9778269.9778
65269.9778269.9778269.9778269.9778269.9778269.9778
66269.9778269.9778269.9778269.9778269.9778269.9778
67809.9334809.9334809.9334809.9334809.9334809.9334
68269.9778269.9778269.9778269.9778269.9778269.9778
69269.9778269.9778269.9778269.9778269.9778269.9778
70269.9778269.9778269.9778269.9778269.9778269.9778
71269.9778269.9778269.9778269.9778269.9778269.9778
72269.9778269.9778269.9778269.9778269.9778269.9778
73269.9778269.9778269.9778269.9778269.9778269.9778
74 11.8790 11.8790 11.8790 11.8790 11.8790 11.8790
Taylor River
75269.9778269.9778269.9778269.9778269.9778269.9778
76269.9778269.9778269.9778269.9778269.9778269.9778
77269.9778269.9778269.9778269.9778269.9778269.9778
78269.9778269.9778269.9778269.9778269.9778269.9778
79269.9778269.9778269.9778269.9778269.9778269.9778
80269.9778269.9778269.9778269.9778269.9778269.9778
81 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978
East Creek
82269.9778269.9778269.9778269.9778269.9778269.9778
83269.9778269.9778269.9778269.9778269.9778269.9778
84269.9778269.9778269.9778269.9778269.9778269.9778
85269.9778269.9778269.9778269.9778269.9778269.9778
86269.9778269.9778269.9778269.9778269.9778269.9778
87269.9778269.9778269.9778269.9778269.9778269.9778
88269.9778269.9778269.9778269.9778269.9778269.9778
89269.9778269.9778269.9778269.9778269.9778269.9778
90269.9778269.9778269.9778269.9778269.9778269.9778
91269.9778269.9778269.9778269.9778269.9778269.9778
92269.9778269.9778269.9778269.9778269.9778269.9778
93269.9778269.9778269.9778269.9778269.9778269.9778
94269.9778269.9778269.9778269.9778269.9778269.9778
95269.9778269.9778269.9778269.9778269.9778269.9778
96269.9778269.9778269.9778269.9778269.9778269.9778
97269.9778269.9778269.9778269.9778269.9778269.9778
98269.9778269.9778269.9778269.9778269.9778269.9778
99269.9778269.9778269.9778269.9778269.9778269.9778
100269.9778269.9778269.9778269.9778269.9778269.9778
101269.9778269.9778269.9778269.9778269.9778269.9778
102269.9778269.9778269.9778269.9778269.9778269.9778
103269.9778269.9778269.9778269.9778269.9778269.9778
104269.9778269.9778269.9778269.9778269.9778269.9778
105269.9778269.9778269.9778269.9778269.9778269.9778
106269.9778269.9778269.9778269.9778269.9778269.9778
107269.9778269.9778269.9778269.9778269.9778269.9778
108269.9778269.9778269.9778269.9778269.9778269.9778
109 40.4967 40.4967 40.4967 40.4967 40.4967 40.4967
Trout Creek
110269.9778269.9778269.9778269.9778269.9778269.9778
111269.9778269.9778269.9778269.9778269.9778269.9778
112269.9778269.9778269.9778269.9778269.9778269.9778
113269.9778269.9778269.9778269.9778269.9778269.9778
114269.9778269.9778269.9778269.9778269.9778269.9778
115269.9778269.9778269.9778269.9778269.9778269.9778
116269.9778269.9778269.9778269.9778269.9778269.9778
117269.9778269.9778269.9778269.9778269.9778269.9778
118269.9778269.9778269.9778269.9778269.9778269.9778
119269.9778269.9778269.9778269.9778269.9778269.9778
120 10.7991 10.7991 10.7991 10.7991 10.7991 10.7991
Shell Creek
121 16.1987 16.1987 16.1987 16.1987 16.1987 16.1987
Stllwater Creek
122269.9778269.9778269.9778269.9778269.9778269.9778
123269.9778269.9778269.9778269.9778269.9778269.9778
124 8.0993 8.0993 8.0993 8.0993 8.0993 8.0993
Orgeon Creek
246
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
125269.9778269.9778269.9778269.9778269.9778269.9778
126 56.6953 56.6953 56.6953 56.6953 56.6953 56.6953
127269.9778269.9778269.9778269.9778269.9778269.9778
128 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978
1 -0.12
10.
1.0
RS11 Bar Init
2
0.03
10.
1.0
3 -0.12
10.
1.0
4
0.03
10.
1.0
5 -0.12
10.
1.0
6
0.03
10.
1.0
7 -0.12
10.
1.0
8
1.52
10.
0.08
9 -0.12
10.
1.0
10
0.03
10.
1.0
11 -0.12
10.
1.0
12 -0.12
10.
1.0
13
0.03
10.
1.0
14 -0.12
10.
1.0
15
1.52
10.
0.05
16
0.03
10.
1.0
17 -0.12
10.
1.0
18
0.03
10.
1.0
19 -0.12
10.
1.0
20
1.52
10. 0.080
21
0.03
10.
1.0
22 -0.12
10.
1.0
23
0.03
10.
1.0
24 -0.12
10.
1.0
25
0.03
10.
1.0
26 -0.12
10.
1.0
27
0.03
10.
1.0
28 -0.12
10.
1.0
29
0.03
10.
1.0
30 -0.12
10.
1.0
31
0.03
10.
1.0
32
1.52
10. 0.080
33 -0.12
10.
1.0
34
0.03
10.
1.0
35
1.52
10. 0.080
36
0.03
10.
1.0
37 -0.12
10.
1.0
38
0.03
10.
1.0
39 -0.12
10.
1.0
40
0.03
10.
1.0
41 -0.12
10.
1.0
42
0.03
10.
1.0
43 -0.12
10.
1.0
44
0.03
10.
1.0
45 -0.01
10.
1.0
46 -0.15
10.
1.0
47 -0.30
10.
1.0
48
1.52
10. 0.080
49 -0.15
10.
1.0
50 -0.30
10.
1.0
51 -0.15
10.
1.0
52 -0.30
10.
1.0
53 -0.15
10.
1.0
54 -0.30
10.
1.0
55 -0.30
10.
1.0
56 -0.30
10.
1.0
57 -0.30
10.
1.0
58 -0.30
10.
1.0
59 -0.30
10.
1.0
60 -0.30
10.
1.0
61 -0.30
10.
1.0
62 -0.30
10.
1.0
63 -0.30
10.
1.0
64 -0.30
10.
1.0
65 -0.30
10.
1.0
66 -0.30
10.
1.0
247
West Highway Creek
East Highway Creek
Alligator Creek
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
1.52
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
1.22
1.22
1.22
1.22
1.22
1.0
0.30
0.03
-0.12
0.03
-0.12
0.03
-0.12
0.03
-0.12
0.03
-0.12
0.03
-0.12
0.03
-0.12
0.03
1.52
-0.12
0.03
-0.12
0.03
-0.12
1.52
0.03
-0.12
0.03
-0.12
0.03
1.52
-0.12
0.03
-0.12
0.03
-0.12
0.03
-0.12
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.040
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.080
1.0
1.0
1.0
1.0
1.0
0.080
1.0
1.0
1.0
1.0
1.0
0.080
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Mud Creek
248
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
0.03
-0.12
0.03
-0.12
1.52
0.03
-0.12
0.03
-0.12
1.52
-0.12
0.03
-0.12
0.03
-0.12
0.03
-0.3
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
1.52
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
1.52
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
-0.30
-0.15
1.52
-0.30
-0.15
-0.30
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
10.
1.0
1.0
1.0
1.0
0.055
1.0
1.0
1.0
1.0
0.020
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.022
1.0
1.0
1.0
1.0
1.0
1.0
0.040
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.120
1.0
1.0
1.0
McCormick
Taylor
East
Trout Creek
249
2 113 -0.15
10.
1.0
2 114 -0.30
10.
1.0
2 115 -0.15
10.
1.0
2 116 -0.30
10.
1.0
2 117 -0.15
10.
1.0
2 118 -0.30
10.
1.0
2 119
-0.1
10.
1.0
2 120
1.52
10. 0.020
Shell Creek
2 121
1.52
10. 0.030
Stillwater Creek
2 122
-0.1
10.
1.0
2 123
-0.1
10.
1.0
2 124
1.52
10. 0.015
Oregon Creek
2 125
-0.1
10.
1.0
2 126
1.52
10. 0.070
West Highway
Creek
2 127
-0.1
10.
1.0
2 128
1.52
10. 0.050
East Highway
Creek
1 5 1 15 1 2 0 60.0SOUTHWEST SHORE SOUTHWEST CORNER
RS12_1
2 8 2 1 78 1 0 60.0SOUTHWEST CORNER SOUTH OF TAYLOR
RS12_2
3 8 79 1137 1 0 60.0SOUTH OF TAYLOR SOUTHEAST CORNER
RS12_3
4 7144 40144 38 0 60.0CULVERTS AT US 1
RS12_4
5 7118 69118 85 0 60.0GW INTERACTION WITH C-111
RS12_5
6 5 25 44 25 69 0 60.0CULVERTS ON WEST SIDE
RS12_6
7 6 30 72 47 72 0 60.0FROM P46 TO CY3
RS12_7
8 6 48 72 68 72 0 60.0FROM CY3 TO P67
RS12_8
1 0.200 15.0 40.0 0.0182
RS13_1
2 0.200 15.0 40.0 0.0143
RS13_2
3 0.200 15.0 40.0 0.0048
RS13_3
4 0.200 15.0 3.6 0.0064
RS13_4
5 0.200 15.0 0.0 0.0053
RS13_5
6 0.200 15.0 0.0 0.004
RS13_6
7 0.200 15.0 0.0 0.004
RS13_7
8 0.200 15.0 0.0 0.004
RS13_8
1 0.200 15.0 40.0 0.0182
RS14_1
2 0.200 15.0 40.0 0.0143
RS14_2
3 0.200 15.0 40.0 0.0048
RS14_3
4 0.200 15.0 3.6 0.0064
RS14_4
5 0.200 15.0 0.0 0.0053
RS14_5
6 0.200 15.0 0.0 0.004
RS14_6
7 0.200 15.0 0.0 0.004
RS14_7
8 0.200 15.0 0.0 0.004
RS14_8
1 5.01 salinity
RS20_1
2 0.005 TP:TSB water mg/L=g/m3=ppm
RS20_2
1
RS21_1
2
RS21_2
1 0.01 0.10 0.20 0.5 1.0 2.0 5.0
RS22_1
2 0.01 0.10 0.20 0.5 1.0 2.0 5.0
RS22_2
0.01 0.10 0.20 0.5 1.0 2.0 5.0
RS23
1.0 2.0
5. 10. 50. 100. 200. 500. 1000. RS24
-0.5 -0.2 -0.1 -0.05 0.001 0.1 0.2 0.5 1.0 RS25
0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.2 1.3
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.7 0.9 1.0 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.4 1.5 1.2 1.0 0.8 0.6
0.8 1.0 1.2 1.5 1.4 1.4 1.3 1.2 1.2 1.2 1.2 0.9 0.8 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6
0.6 0.7 0.9 1.0 1.1 1.2 1.4 1.5 1.7 1.8 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.3
1.2 1.0 0.9 0.8 0.7 0.6 0.5 0.7 0.9 0.9 1.0 1.1 1.1 1.2 1.2 1.2 1.2 1.3 1.4 1.2 0.9 0.7 0.6
1.3 1.3 1.5 1.5 1.4 1.4 1.3 1.2 1.2 1.2 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6
0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.9 1.9 1.8 1.9
1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
1.9 1.9 1.9 1.9 1.9 1.9 0.1 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2
1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.7 0.8 0.8 0.7 1.0 1.1 1.1 1.1 1.1 1.2 1.4 1.3 1.3 1.0 0.7 0.6
1.0 1.0 1.0 1.0 1.1 1.0 0.9 0.8 0.7 1.0 1.0 0.9 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.8 1.8 1.7 1.8
1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
250
1.9 1.8 1.8 1.8 1.8 0.1 0.1 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 0.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.1 1.2
1.1 0.9 0.8 0.7 0.7 0.6 0.5 0.6 0.8 0.7 -0.1 0.9 1.0 1.0 1.1 1.1 1.1 1.2 1.2 1.0 1.0 0.6 0.6
1.0 1.0 1.0 1.0 1.1 1.2 1.2 0.1 0.7 0.8 0.9 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.0 1.0 0.1 0.4 0.5
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.8
1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 0.2 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.1
1.1 0.9 0.7 0.7 0.6 0.5 0.5 0.6 0.8 0.6 0.1 0.2 0.9 1.0 1.0 1.0 1.0 1.1 1.1 1.0 0.5 0.6 0.6
0.6 0.7 1.0 0.9 1.0 1.1 1.0 0.9 1.0 0.7 0.7 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.1 0.2
0.1 -0.2 0.6 0.6 1.0 1.2 1.3 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.6 1.7
1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.1 1.7 1.7 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 0.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.1
1.0 -0.2 0.7 0.6 0.6 0.5 0.5 0.6 0.7 0.6 0.6 0.1 0.9 0.9 0.9 0.9 0.9 1.1 1.0 0.4 0.1 0.1 0.1
0.1 0.1 0.1 0.7 1.0 1.0 1.0 0.7 1.0 0.1 1.0 1.0 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.0 1.0 0.7 0.6
0.1 0.0 0.4 0.4 0.8 1.2 1.2 1.4 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 0.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 1.0
1.0 -0.2 0.6 0.6 0.5 0.5 0.5 0.6 0.7 0.5 0.6 -0.1 0.8 0.8 0.9 0.8 0.8 1.0 0.4 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.7 0.8 0.9 0.9 1.0 0.1 0.1 1.0 1.0 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.1 1.0 1.0 0.4
0.4 0.1 0.1 0.1 0.4 1.1 1.2 1.4 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 0.1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.7 0.1 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 0.1 0.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9
0.9 -0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.5 -0.4 -0.2 0.8 0.8 0.8 0.7 0.7 0.2 0.1 0.1 0.1 0.2 0.5
0.7 0.7 0.7 0.8 0.7 1.5 1.5 0.1 0.1 0.1 0.9 0.9 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.0
0.4 0.4 0.0 0.4 1.0 1.1 1.2 1.4 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 0.1 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9
0.9 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.4 0.1 0.6 0.7 0.7 0.7 0.6 0.1 0.1 0.2 0.1 0.7 0.7 0.7
0.7 0.8 0.7 0.1 0.0 1.5 1.5 0.4 0.2 0.1 0.1 0.1 1.0 1.0 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.1
1.0 0.5 0.5 -0.1 1.0 1.1 1.2 1.3 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 0.1 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.8 0.8
0.8 -0.2 0.4 0.5 0.4 0.4 0.4 0.5 0.6 0.3 0.0 0.6 0.6 0.6 0.6 0.6 0.0 0.1 0.1 0.1 0.7 0.7 0.7
0.7 0.8 0.7 0.1 0.2 1.5 1.5 0.2 0.1 0.1 0.1 0.1 0.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1
1.1 1.0 1.0 -0.1 -0.1 1.1 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 0.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 0.1 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8
0.8 -0.2 0.0 0.4 0.4 0.4 0.4 0.5 0.6 0.3 0.0 0.6 0.6 0.6 0.6 0.1 0.1 0.1 0.1 0.6 0.7 0.6 0.6
0.4 0.8 0.7 0.6 0.2 1.5 1.5 0.4 0.1 0.1 0.1 0.1 0.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1.1 1.1 1.1 1.0 -0.1 1.2 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4
1.3 1.3 0.9 1.5 1.5 1.5 -0.1 1.5 1.5 1.6 1.6 1.6 1.6 1.6 0.2 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 0.1 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 -0.2 0.4 0.4 0.6 0.6 0.6 0.7 0.7
0.7 0.6 0.1 0.4 0.4 0.4 0.4 0.5 0.6 -0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.6 0.7 0.7 0.1
1.5 1.5 0.7 0.4 0.1 0.2 0.4 0.2 0.1 0.0 0.1 0.1 0.1 1.2 1.1 1.1 1.1 1.2 1.1 1.0 1.0 1.0 1.5
1.5 1.0 1.0 1.0 0.0 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.3 1.2
1.1 1.0 -0.1 0.9 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 0.2 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 -0.1 0.1 0.0 -0.1 0.4 0.6 0.6 0.7
0.7 0.5 -0.1 0.0 0.1 0.1 -0.2 -0.2 -0.1 0.0 0.0 -0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.0 0.1 0.4 0.1 0.1
1.5 1.5 0.7 0.0 -0.1 -0.1 0.1 0.1 -0.1 0.3 0.2 0.2 -0.1 0.0 1.0 1.1 1.1 1.1 0.9 0.1 1.0 1.0 1.5
1.5 1.0 1.0 1.0 0.1 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.2 0.0
0.0 0.0 0.0 0.9 1.4 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6
251
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 -0.1 0.0 0.9 0.1 0.1 0.3 0.1 0.6 0.6
0.6 0.5 -0.3 0.0 0.1 0.9 1.5 1.5 1.5 1.5 1.5 0.3 0.4 0.4 0.3 0.2 0.1 0.1 0.1 0.1 0.7 0.8 0.8
1.5 1.5 0.1 0.0 0.0 0.1 0.1 0.2 0.3 0.3 0.3 0.2 0.0 -0.1 -0.1 1.0 1.0 1.1 1.1 0.1 0.1 0.9 1.5
1.5 0.7 1.0 0.1 0.1 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 0.0 0.0
0.0 -0.1 -0.1 1.0 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 -0.2 -0.1 0.1 0.1 1.5 1.5 1.5 1.5 0.1 0.6
0.6 0.4 0.4 0.0 0.1 0.9 1.5 1.5 1.5 1.5 1.5 0.9 0.9 0.9 0.9 0.1 0.1 0.1 0.1 0.1 0.4 1.5 1.5
1.5 1.5 0.6 0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.0 1.0 1.1 0.0 0.1 0.9 1.5
1.5 0.0 0.0 0.1 0.1 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 -0.1 -0.1 0.1 0.0 0.0 1.0 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 -0.1 -0.1 0.1 0.1 0.0 1.5 1.5 1.5 1.5 0.6 0.6
0.6 0.6 1.5 1.5 1.5 1.5 1.5 1.5 0.1 1.5 1.5 0.9 0.6 0.9 0.6 0.1 0.1 0.1 0.1 0.4 0.5 1.5 1.5
0.1 1.5 1.5 1.5 1.5 0.3 0.1 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.2 0.1 0.1 1.0 0.0 0.1 0.0 0.1
0.1 0.1 0.1 0.1 0.1 0.1 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 -0.1 0.0 1.0
1.0 1.1 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4
1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 0.0 0.1 -0.1 -0.1 -0.1 -0.1 0.0 -0.1 -0.2 -0.2 -0.2 0.1 0.1 0.1 0.1 0.2 0.3 0.3 0.3 0.6 0.6
0.6 0.6 1.5 1.5 1.5 1.5 1.5 1.5 0.1 1.5 1.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.7 0.8 1.5 1.5 1.5
1.5 1.5 1.5 1.5 1.5 0.9 0.0 0.2 0.5 0.2 0.4 0.4 0.5 0.3 0.4 0.4 0.3 0.1 0.2 0.2 0.2 0.2 0.1
0.1 0.9 0.1 0.1 0.1 0.1 0.0 -0.1 -0.1 0.0 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
1.3 1.3 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.2 -0.2 -0.2 -0.1 -0.2 -0.2 -0.3 -0.3 -0.2 -0.1 -0.1 0.0 0.0 0.1 0.1 0.2 0.1 0.0 0.0 0.3 0.6 0.6
0.6 0.6 0.6 0.6 -0.1 0.3 0.4 0.1 0.0 1.5 1.5 0.1 0.0 0.0 0.1 0.1 0.9 0.9 0.9 0.9 1.5 1.5 1.5
1.5 0.9 0.9 1.5 1.2 0.9 0.1 0.0 0.5 0.6 0.5 0.5 0.4 0.4 0.4 0.5 0.7 0.5 0.5 0.4 0.4 0.2 0.1
0.1 1.0 1.0 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.2 -0.1 -0.1 -0.1 -0.1 1.2 1.2 1.2 1.2
1.2 1.1 1.1 1.1 1.2 1.2 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3
1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 -0.1 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 0.9
-0.4 -0.3 -0.2 -0.1 -0.1 -0.1 0.0 0.0 0.0 1.5 1.5 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.9 0.9 0.8 0.7 0.1
0.9 0.9 0.1 0.0 0.9 0.9 0.9 0.1 0.3 0.5 0.4 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.3 0.2 0.2
0.1 -0.1 1.0 1.1 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.0 -0.1 -0.1 -0.1 -0.1 0.0 0.0 1.0 1.1 1.1 1.1
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 -0.4
-0.4 -0.3 -0.2 -0.1 -0.1 -0.1 -0.1 0.0 0.0 1.5 1.5 -0.1 0.0 0.0 0.0 0.0 0.0 0.6 0.1 0.2 0.1 0.1 0.1
0.1 0.1 0.1 0.7 0.9 0.9 0.9 0.9 0.2 0.4 0.3 0.2 0.3 0.4 0.4 0.3 0.2 0.2 0.4 0.4 0.2 0.2 0.2
0.1 0.0 0.1 0.1 1.0 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.3 1.2 1.2 1.1 1.1 1.0 0.0 0.1 1.0 1.0 1.0
1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.0 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.2 0.5 0.4 0.4 1.2 1.2 1.2
1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 -0.1 -0.1 0.1 0.0 -0.1 -0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.0 -0.1 -0.2 -0.2
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 0.1 0.1 0.1
0.9 0.1 0.1 1.0 1.0 0.9 0.9 0.2 0.1 0.3 0.3 0.3 0.4 0.5 0.2 0.2 0.1 0.1 0.4 0.3 0.1 0.0 0.0
0.2 0.4 0.2 0.1 1.2 1.2 1.2 1.5 1.5 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 0.2 0.2 1.0 1.1
1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.3 0.3 1.2
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1
1.1 1.1 1.0 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.1 0.1 0.1 0.0 -0.1 -0.1 -0.1 -0.1 0.1 0.0 0.0 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 -0.1 -0.3 -0.2 -0.1
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 0.0 -0.1 0.1 0.1 0.0
0.1 0.1 1.0 1.0 0.9 0.9 0.9 0.2 0.3 0.2 0.5 0.5 0.3 0.3 0.2 0.2 0.3 0.5 0.7 0.5 0.3 0.0 0.2
0.2 0.2 0.2 0.1 0.1 0.9 0.0 1.5 1.5 1.1 1.2 1.3 1.3 1.4 1.4 1.3 1.3 1.2 1.2 1.1 0.4 0.4 0.3
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.4 1.2 1.2
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.2 1.2
1.1 1.1 1.0 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.0 0.0 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0
1.5 1.5 0.1 0.0 1.5 1.5 0.9 0.7 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.9 0.9 -0.1 -0.1 -0.1 0.0 0.1 0.9 0.9
0.9 0.9 0.9 0.9 0.9 0.2 0.2 0.2 0.2 0.3 0.4 0.4 0.2 0.4 0.2 0.2 0.2 0.4 0.5 0.5 0.5 0.4 0.2
0.3 0.4 0.2 0.2 0.2 0.2 0.2 1.5 1.5 0.1 -0.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.1 1.1 0.2 0.9 0.9
0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 0.4 1.0 1.1 1.1
252
1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 0.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.0 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 0.1 0.0
1.5 1.5 0.9 0.9 1.5 1.5 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 -0.1 0.0 0.9 0.9 0.9 0.0 0.4 0.9 0.9 0.9 0.9
0.9 0.9 0.9 0.9 0.1 0.2 0.2 0.2 0.1 0.3 0.4 0.5 0.4 0.4 0.3 0.2 0.2 0.5 0.5 0.5 0.5 0.4 0.3
0.3 0.5 0.2 0.2 0.3 0.4 0.3 1.5 1.5 0.1 -0.1 0.1 1.0 0.2 1.5 1.5 1.1 1.1 1.1 1.1 0.3 0.9 0.9
0.0 1.0 1.0 1.0 1.0 1.0 0.9 0.0 0.1 0.0 0.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1
1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0
1.0 1.0 0.2 0.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.1 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.1 0.0 0.1 0.3 0.0
1.5 1.5 0.0 0.9 1.5 1.5 1.5 -0.1 -0.2 -0.2 -0.4 -0.1 0.4 0.9 0.0 0.0 0.9 0.2 0.1 0.9 0.9 0.9 1.0
0.9 0.9 0.9 0.1 0.1 0.2 0.2 0.3 0.1 0.3 0.4 0.5 0.9 0.5 0.4 0.4 0.5 0.9 0.3 0.3 0.3 0.1 0.2
0.2 0.2 0.1 0.2 0.5 0.7 0.3 0.3 0.9 0.3 0.1 0.1 0.2 0.2 1.5 1.5 1.0 1.0 1.0 1.0 0.4 0.3 0.9
0.2 0.2 1.0 1.0 1.0 1.0 0.1 0.0 0.1 0.0 0.1 0.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1
1.1 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 0.2 0.2 0.2 1.0 -99.9 -99.9 -99.9 -99.9
-99.9 -0.2 -0.1 -0.1 0.0 0.0 -0.1 -0.1 0.0 -0.1 -0.1 -0.1 -0.1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.4 0.3
1.5 1.5 0.9 -0.1 1.5 1.5 1.5 0.9 0.9 0.6 0.6 0.7 0.7 0.5 0.2 0.1 0.2 0.2 0.0 0.2 0.9 0.9 0.9
0.9 0.9 0.9 -0.1 0.1 0.2 0.3 0.4 0.5 0.2 0.2 0.3 0.4 0.5 0.4 0.4 0.5 -0.1 0.5 0.5 0.4 0.2 0.2
0.2 0.2 0.2 0.4 0.4 0.3 0.4 0.4 0.3 0.4 0.4 0.3 0.3 0.4 1.5 1.5 0.4 0.4 0.4 1.0 0.4 0.3 0.6
0.3 0.2 0.0 0.0 1.0 1.0 0.0 1.0 1.0 0.0 0.1 0.2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.4 1.0 1.1 1.1
1.1 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.0 0.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 0.2 1.0 1.0 1.0 1.0 1.0 -99.9 -99.9 -99.9
-99.9 -99.9 0.0 0.0 0.0 0.0 0.0 -0.1 0.9 0.9 0.9 0.6 0.9 0.9 0.9 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9
0.9 0.9 0.9 -0.1 -0.1 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 0.7 0.4 0.2 0.4 0.4 0.2 0.1 0.7 0.9 0.9
0.9 0.0 -0.1 0.0 0.2 0.1 0.3 0.4 0.4 0.4 0.4 0.4 0.3 0.5 0.5 0.5 0.4 0.3 0.4 0.3 0.2 0.1 0.4
0.4 0.4 0.4 0.4 0.5 0.6 0.3 0.9 0.4 0.3 0.3 0.6 0.3 0.4 1.5 1.5 0.4 0.4 0.4 0.5 0.4 0.9 0.9
0.9 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 0.1 0.1 0.2 1.0 1.0 1.0 1.0 1.0 1.0 0.5 1.0 1.0 1.1 1.1
1.1 1.1 1.1 1.1 1.2 1.0 1.0 1.0 0.1 0.1 1.0 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.1 0.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 -99.9
-99.9 -99.9 -99.9 0.1 0.0 0.0 0.0 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.1 1.1 1.2 1.1 1.1 1.1 1.0 1.0
0.9 0.9 0.9 0.9 -0.1 -0.1 0.9 0.9 0.9 1.0 1.0 1.0 0.9 0.9 0.9 0.3 0.3 0.4 0.4 0.4 0.2 0.1 0.1
0.9 0.9 0.1 0.0 0.0 0.3 0.2 0.3 0.3 0.3 0.5 0.5 0.5 0.5 0.6 0.7 0.6 0.5 0.5 0.5 0.4 0.3 0.3
0.5 0.5 0.5 0.6 0.5 0.7 0.8 1.1 0.6 0.5 0.4 0.4 0.6 0.4 0.9 0.9 0.9 0.5 0.4 0.3 0.4 0.4 0.9
0.9 0.9 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 1.0 0.1 0.1 1.0 1.0 1.0 1.0 0.3 0.3 0.5 1.0 1.0 1.1
1.1 1.1 1.1 1.1 1.1 1.1 1.0 0.2 0.1 0.1 0.1 0.9 1.5 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.1 0.1 1.1 1.1 1.1 1.1 1.2 1.2 1.1 1.1 1.1
-99.9 -99.9 -99.9 -99.9 -99.9 0.0 0.0 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9
0.9 0.9 0.1 0.1 -0.1 -0.1 -0.1 0.0 0.9 0.3 0.4 0.4 0.5 0.7 0.9 0.1 0.5 0.4 0.4 0.5 0.2 0.2 0.1
0.0 0.2 0.2 0.1 0.9 0.3 0.3 0.3 0.3 0.4 0.5 0.5 0.6 0.8 0.8 0.8 0.8 0.8 0.7 0.5 0.5 0.6 0.4
0.8 0.7 0.6 0.8 0.6 0.9 1.1 1.2 1.0 0.5 0.4 0.3 0.3 0.9 0.9 0.9 0.9 0.4 0.3 0.3 0.5 0.9 0.9
0.9 0.9 0.9 0.0 0.7 0.7 1.0 1.0 1.0 1.0 1.0 0.1 0.7 1.0 1.0 1.0 0.4 0.4 0.3 1.0 1.0 1.0 1.1
0.6 1.1 1.1 1.1 1.1 1.1 1.0 0.2 0.1 0.9 0.9 0.6 1.5 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.1 0.0
0.1 1.1 1.1 1.1 1.2 1.2 1.2 1.1 1.1 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.1 0.0 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
0.9 0.1 0.1 0.1 0.3 0.2 0.1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.3 0.5 0.3 0.3 0.3 0.2 0.1 0.1
0.0 0.5 0.4 0.2 0.2 0.4 0.4 0.3 0.2 0.8 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.2 0.1 0.3 0.4 0.8
0.5 0.5 0.6 0.6 0.6 0.6 0.4 0.4 0.5 0.4 0.3 0.2 0.6 0.9 0.9 0.9 0.2 0.2 0.4 0.9 0.7 0.9 0.3
0.9 0.2 0.1 0.9 1.1 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 1.0 1.0 0.3 0.4 0.3 1.0 1.0 1.5 1.5
1.0 1.0 1.0 1.0 1.1 1.1 0.1 0.2 0.1 0.1 0.1 0.1 1.5 1.5 0.1 0.4 1.0 0.1 0.1 0.1 0.1 0.1 0.0
1.0 1.1 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.0 0.0 0.0 0.0 0.1 -0.1 0.0 0.9 0.2 0.3 0.3 0.2 0.9
0.2 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.7 0.0 0.1 0.1 0.1 0.2 0.4 0.4 0.4 0.3 0.1 0.3 0.2 0.2
0.2 0.4 0.3 0.2 0.2 0.2 0.4 0.4 0.3 0.5 0.2 0.4 0.4 0.2 0.4 0.4 0.4 0.3 -0.1 0.2 0.3 0.3 0.4
0.5 0.4 0.3 0.4 0.4 0.6 0.6 0.6 0.4 0.4 0.3 0.0 0.1 0.2 0.2 0.2 0.2 0.3 0.4 0.5 0.9 0.9 0.3
0.2 0.1 0.1 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.1 0.5 0.1 0.2 0.2 0.4 0.3 0.4 0.4 0.4 0.7 1.5 1.5
1.0 1.0 1.0 1.0 1.1 1.0 0.2 0.4 0.1 0.1 0.2 0.4 1.5 1.5 0.9 0.1 0.1 0.1 0.1 0.0 0.1 0.0 1.0
1.1 1.2 1.3 1.4 1.4 1.4 1.3 1.2 1.1 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.1 0.1 0.0 0.0 0.0 0.1 0.3 0.3 0.3 0.3 0.3 0.3
0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.4 0.5 0.5 0.4 0.3 0.1 0.2 0.2 0.2
0.3 0.3 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.4 0.3 0.4 0.4 0.2 0.3 0.4 0.4 0.4 0.1 0.2 0.3 0.3 0.4
0.4 0.3 0.2 0.3 0.4 0.6 0.6 0.4 0.3 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.9 0.5 0.9 0.5 0.3
0.2 0.1 0.1 1.4 1.4 1.4 1.4 1.4 1.3 1.2 1.2 1.0 0.2 0.2 0.3 1.0 1.0 0.9 0.9 1.1 0.9 1.5 1.5
0.2 1.0 1.0 1.0 1.0 0.3 0.6 0.6 0.4 0.2 0.1 0.1 1.0 1.0 1.0 1.0 0.5 0.6 0.7 0.5 0.5 0.1 1.0
1.1 1.2 1.4 1.4 1.4 1.4 1.4 1.2 1.2 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.9 0.9 0.1 0.1 0.4 0.4 0.3 0.3 0.5
0.5 0.4 0.3 0.2 0.4 0.3 0.2 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.7 0.5 0.4 -0.1 0.2 0.2
0.2 0.3 0.3 0.2 0.3 0.4 0.4 0.5 0.5 0.5 0.4 0.5 0.5 0.5 0.2 0.2 0.3 0.4 0.5 0.3 0.2 0.3 0.4
0.4 0.4 0.3 0.3 0.3 0.6 0.5 0.5 0.2 0.4 0.3 0.3 0.5 0.5 0.4 0.3 0.3 0.3 0.3 0.4 0.5 0.5 0.5
0.3 0.1 0.1 1.4 1.5 1.5 1.4 1.4 1.2 1.3 1.6 1.2 1.2 0.2 0.2 0.2 1.1 1.1 1.0 1.1 1.4 1.0 1.5
253
1.5 1.1 0.2 1.0 1.0 0.2 0.6 1.0 0.9 0.5 0.9 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.1 1.3 1.2 1.0 0.5
0.1 0.4 1.2 1.2 1.4 1.4 1.4 1.4 1.2 1.1 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.1 0.1 0.2 0.2 0.3 0.3 0.8
0.7 0.4 0.3 0.1 0.1 0.1 0.2 0.2 -0.1 0.6 0.5 0.5 0.7 0.6 0.6 0.6 0.5 0.5 0.3 0.2 0.4 0.2 0.1
0.1 0.1 0.3 0.5 0.5 0.5 0.4 0.4 0.5 0.5 0.4 0.5 0.4 0.2 -0.1 0.2 0.0 0.1 0.3 0.4 0.4 0.3 0.3
0.4 0.3 0.3 0.4 0.5 0.7 0.5 0.4 0.7 0.4 0.1 0.1 0.3 0.3 0.4 0.4 0.3 0.3 0.2 0.4 0.3 0.5 0.8
0.9 0.1 1.1 1.4 1.3 1.3 1.4 1.4 1.4 1.3 1.2 1.2 1.2 1.2 0.9 0.9 1.0 1.3 1.0 1.2 1.2 1.4 1.3
1.4 0.7 0.2 0.2 0.2 0.2 0.4 0.9 0.9 0.9 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.3 1.3 1.2
1.1 1.1 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.0 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.2 0.2 0.3 0.4 0.5 0.6
0.5 0.3 0.3 0.4 0.8 0.3 0.2 0.2 0.5 0.6 0.7 0.7 0.3 0.6 0.4 0.4 0.6 0.7 0.5 0.3 -0.1 0.1 0.2
0.2 0.1 0.4 0.3 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.4 0.3 0.2 0.3 0.2 0.2 0.4 0.3 0.3 0.3 0.3
0.4 0.3 0.3 0.3 0.2 0.4 0.3 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.5 0.4 0.4 0.7 0.4
0.3 0.2 1.2 1.2 1.1 1.1 1.2 1.4 1.4 1.3 1.4 1.5 1.3 1.3 1.2 1.4 1.2 1.4 1.4 1.2 1.3 1.5 1.5
1.3 0.9 0.3 0.2 0.3 0.2 0.3 0.9 0.9 0.9 0.2 0.2 0.1 1.0 1.0 1.0 0.0 1.0 1.0 1.1 1.2 1.2 1.3
1.3 1.3 1.2 1.2 0.1 0.1 0.1 0.2 0.2 0.2 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.2 0.3 0.4 0.5
0.4 0.3 0.3 0.4 0.5 0.3 0.3 0.3 0.3 0.6 0.7 0.7 0.5 0.5 0.4 0.4 0.5 0.5 0.5 0.3 0.1 0.1 0.2
0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.5 0.4 0.4 0.3 0.3 0.2 0.3 0.4 0.3 0.3 0.3 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.4 0.4 0.4 0.5 0.4
0.3 0.2 0.5 0.5 0.2 0.1 1.1 1.0 1.2 1.4 1.4 1.3 1.3 1.3 1.3 1.5 1.4 1.5 1.5 1.4 1.5 1.1 1.5
1.2 1.0 0.9 0.2 0.2 0.3 0.9 0.9 0.4 0.9 0.3 0.2 0.1 0.2 0.1 0.1 0.1 0.1 1.0 1.0 1.0 1.0 1.1
1.1 1.1 1.3 1.3 1.2 1.1 1.0 0.2 0.2 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.2 0.3 0.5
0.3 0.4 0.3 0.2 0.4 0.4 0.4 0.3 0.2 0.6 0.7 0.7 0.7 0.4 0.5 0.5 0.5 0.3 0.4 0.3 0.2 0.1 0.3
0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.4 0.4 0.4 0.3 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.4 0.3 0.3 0.3 0.4
0.4 0.2 0.3 0.3 0.2 0.1 0.1 0.2 1.2 1.2 1.3 1.4 1.2 1.2 1.2 1.4 1.5 1.5 0.9 1.1 1.2 0.8 1.2
1.0 1.2 0.9 0.2 0.3 0.3 0.9 0.9 0.5 0.4 0.3 0.9 0.2 0.2 0.2 0.2 0.2 0.9 0.1 0.1 0.1 1.0 1.1
1.1 1.2 1.2 1.3 1.3 1.2 1.1 1.0 0.2 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.3 0.3
0.1 0.9 0.5 0.4 0.3 0.1 0.6 0.4 0.2 0.3 0.4 0.5 0.6 0.6 0.2 0.5 0.5 0.5 0.4 0.2 0.2 0.0 0.5
0.5 0.4 0.3 0.4 0.4 0.4 0.3 -0.1 0.4 0.4 0.4 0.3 0.4 0.4 0.4 0.4 0.5 0.5 0.4 0.4 0.4 0.4 0.3
0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.5 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3
0.5 0.4 0.3 0.3 0.5 0.3 0.2 0.1 0.1 1.1 1.2 1.2 1.3 0.6 1.1 1.1 1.4 1.4 1.4 1.1 0.1 0.5 0.5
0.9 0.9 0.3 0.3 0.3 0.4 0.5 0.3 0.1 0.3 0.2 0.4 0.4 0.5 0.2 0.9 0.9 0.2 0.9 0.2 0.2 0.1 0.2
1.0 1.1 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.0 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.1 0.2 0.6 0.6 0.8 0.5 0.5 0.5 0.7 0.7 0.1 0.3 0.2 0.6 0.6 0.5 0.4 0.2 0.1 0.2 0.2 0.2 0.5
0.3 0.4 0.5 0.4 0.5 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.5 0.4 0.4 0.3
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.3
0.3 0.2 0.3 0.3 0.3 0.3 0.5 0.3 0.2 0.9 1.1 1.1 1.0 0.3 1.0 1.2 1.4 1.2 1.2 0.1 0.1 0.9 0.9
0.9 0.2 0.4 0.3 0.4 0.9 0.3 0.2 0.5 0.2 0.2 0.9 0.3 0.5 0.4 0.2 0.2 0.4 0.2 0.2 0.1 0.2 0.3
0.1 0.2 0.2 1.5 1.5 1.3 1.2 1.2 1.1 1.0 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 0.2 0.4 0.5 0.4 0.4 0.4 0.5 0.6 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.3 0.3 0.3 0.3 0.3 0.4 0.4
0.4 0.4 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.3
0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 1.0 0.2 0.4 1.0 1.1 1.1 0.3 0.3 0.3 0.2 0.1 0.1
0.2 0.2 0.3 0.4 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.5
0.9 0.9 0.2 1.5 1.5 1.1 1.0 1.0 1.0 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 0.3 0.3 0.2 0.2 0.3 0.4 0.2 0.5 0.5 0.5 0.2 0.4 0.4 0.3 0.3 0.5 0.3 0.3 0.5 0.4
0.3 0.3 0.4 0.5 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.1 0.1 0.2
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 1.0 1.0 0.4 0.4 0.4 0.2 0.2 0.2
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 0.3 0.3 0.4 0.3 0.3 0.4 0.5
0.4 0.2 0.9 1.5 1.5 0.2 0.2 1.0 1.0 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.2 0.1 0.0 0.1 0.2 0.1 0.6 0.5 0.6 0.6 0.3 0.2 0.2 0.2 0.0 0.4 0.4 0.3 0.4
0.3 0.3 0.3 0.4 0.5 0.4 0.3 0.4 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.1 0.2 0.4 0.4 0.3 0.3
0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 -0.1 0.2 0.5 0.2 0.2 0.2 0.2
0.3 0.3 0.3 0.5 0.4 0.3 0.3 0.3 0.2 0.4 0.4 0.6 0.6 0.0 0.2 0.3 0.2 0.2 0.3 0.4 0.5 0.2 0.2
0.2 0.1 0.1 0.2 0.2 0.2 0.1 0.0 0.0 -0.1 0.1 0.2 0.2 0.3 0.4 0.2 0.2 0.2 0.4 0.2 0.3 0.4 0.9
0.3 0.2 0.1 1.5 1.5 0.9 0.2 0.4 0.4 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.2 0.2 0.3 0.5 0.2 0.4 0.5 0.9 0.5 0.2 0.2 0.5 0.4 0.4 0.3 0.2 0.3
0.4 0.4 0.4 0.6 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.1 0.2 0.2 0.1 0.2 0.3 0.4 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2
0.3 0.2 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.4 0.5 0.4 0.3 0.2 0.3 0.5 0.5 0.5 0.4 0.5 0.4 0.3 0.2
254
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.3 0.2 0.4 0.6 0.3 0.9 0.9 0.2 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.5 0.4 0.4 0.2 0.4 0.5 0.5 0.5 0.5 0.3 0.2 0.4 0.4 0.4 0.3 0.3 0.4
0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.5 0.4 0.3 0.3 0.4 0.5 0.4 0.4 0.4 0.4 0.3 0.3
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.3 0.4 0.5 0.6 0.4 0.4 0.3 0.2 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.7 0.5 0.4 0.2 0.4 0.5 0.5 0.4 0.5 0.3 0.3 0.4 0.4 0.4 0.3 0.3 0.4
0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.5 0.4 0.4 0.3 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3
0.3 0.3 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.1
0.2 0.3 0.3 0.4 0.9 0.3 0.4 0.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.5 0.5 0.4 -0.1 0.1 0.4 0.5 0.6 0.5 0.4 0.4 0.5 0.4 0.3 0.3 0.3 0.4
0.4 0.3 0.3 0.5 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.2 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3
0.3 0.3 0.3 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.4 0.3 0.4 0.3 0.3 0.3 0.3 0.3
0.3 0.4 0.2 0.2 0.3 0.4 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2
0.2 0.2 0.2 0.3 0.4 0.5 0.5 0.5 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.4 0.4 0.4 0.2 0.4 0.4 0.5 0.5 0.5 0.4 0.3 0.1 0.4 0.3 0.3 0.3 0.3
0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.2 0.2
0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.3 0.2 0.3 0.3
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.5 0.4 0.3 0.2 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.3 0.3 0.4 0.4 0.3 0.3 0.4 0.3 0.4 0.3 0.3 0.2 0.1 0.2 0.2 0.3 0.3
0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2
0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.1 0.2
0.2 0.2 0.2 0.2 0.3 0.3 0.1 -0.6 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.2 0.2 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.1 0.2 0.2 0.2 0.2
0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2
0.2 0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.3 0.3 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.1 -0.4 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.1 0.1 0.1 0.5 0.1 0.4 0.3 0.2 0.2 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.3 0.2 0.3 0.3 0.2 0.3 0.2 0.2
0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3
0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 -0.2 0.2 0.3 0.3 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2
0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.2 0.2 0.3 0.4 0.3 0.2
0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.0 0.1 0.3 0.2 0.2 0.2 0.2 0.2 0.2
0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.1 0.3 0.1 0.0 0.1 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.2 0.2 0.2 0.2 0.2 0.1 0.0 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.1 0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.1
0.1 0.2 0.1 0.1 0.2 0.1 0.0 0.1 0.1 0.0 0.1 0.1 0.1 0.0 0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2
0.2 0.1 0.2 0.2 0.1 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1
0.1 0.1 0.1 0.2 0.2 0.2 0.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 0.9 0.9 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.1 0.1
0.2 0.2 0.1 0.1 0.1 0.1 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2
0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.3 0.2 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
255
0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1
0.1 0.1 0.1 0.1 0.2 0.2 0.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
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-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -0.3 0.4 0.4 -0.2
-0.1 -0.1 -0.1 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -0.2
-0.1 -0.1 -0.1 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 0.0 0.0 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.005
RS28 VIS COEF
RS29 END VISC
0.
1
RS30 DIF COEF
RS31 END DIFF
0.400
RS32 MAN COEF
1
RS33 Flag VEGMANNING
260
0.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 137
2 138
2 138
2 138
2 139
2 139
2 140
2 140
2 141
2 141
2 142
2 142
3 144
4 145
6 147
7 146
8 146
10 146
11 146
13 145
15 145
16 145
18 145
19 143
20 143
22 143
23 143
25 143
26 143
26 143
26 143
26 143
26 143
26 143
26 143
26 143
26 143
26 143
26 142
26 142
26 142
26 142
26 142
26 140
26 138
26 136
26 133
26 130
26 127
26 125
26 122
26 119
26 117
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
RS33 END MANN
RS34 BEN VALU
RS35 END BENV
RS36 END CONC
RS37 END TITL
RS39A COMP ROWS
261
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
26 115
26 115
26 117
28 117
29 117
69 117
69 117
77 117
77 117
78 117
78 117
79 117
79 117
80 117
80 117
81 117
81 117
82 117
83 117
84 115
84 114
85 113
85 112
86 110
91 109
93 108
95 104
96 104
98 104
99 104
102 104
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
25
26
27
27
28
29
30
31
32
32
33
34
35
35
36
36
37
38
38
39
39
40
41
41
69
70
71
71
71
71
71
71
71
71
71
71
71
71
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
END RS39A
RS40A COMP COLS
262
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
72
73
73
73
73
73
73
73
74
75
77
79
81
83
85
86
89
90
90
90
91
91
91
91
92
92
93
93
94
95
95
96
96
96
97
97
97
92
92
92
92
91
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
263
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
11
15
17
19
21
23
24
25
26
26
90
89
89
88
87
86
85
85
66
66
65
65
64
64
63
63
62
62
61
61
61
61
60
60
60
60
59
59
58
58
57
57
57
52
36
36
33
30
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
END RS40A
0
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
5
5
5
5
0
1
1
1
1
1
1
1
1
2
15.000
0.200
0.200
0.200
0.200
0.200
-0.070
0.089
0.269
0.200
0.200
0.200
0.200
0.200
0.089
0.269
0.314
1 -1.00
2 0.00
3 -6.94
4 -0.20
30.000
0.199
0.199
0.199
0.199
0.200
-0.070
0.089
0.269
0.199
4
0.00 140.000
22.820 0.01722
22.820 0.01232
22.820 0.00475
7.310 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
22.820 0.01722
22.820 0.01232
16.660 0.00475
7.310 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
0.00
0.00
0.00
1
0.01 136.000
22.785 0.01722
22.785 0.01232
22.785 0.00475
7.295 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
22.785 0.01722
264
2
2
2
2
2
2
2
5
0
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
5
0
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
0.199
0.199
0.199
0.200
0.089
0.269
0.314
4 -0.10
45.000
0.199
0.199
0.199
0.199
0.200
-0.070
0.089
0.269
0.199
0.199
0.199
0.199
0.200
0.089
0.269
0.314
4 -0.10
60.000
0.199
0.199
0.199
0.199
0.200
-0.070
0.089
0.269
0.199
0.199
0.199
0.199
0.200
0.089
0.269
0.314
22.785 0.01232
16.710 0.00475
7.295 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
1
0.01 112.000
22.750 0.01722
22.750 0.01232
22.750 0.00475
7.280 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
22.750 0.01722
22.750 0.01232
16.760 0.00475
7.280 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
1
0.01 127.000
22.715 0.01722
22.715 0.01232
22.715 0.00475
7.265 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
22.715 0.01722
22.715 0.01232
16.810 0.00475
7.265 0.00683
0.000 0.005
0.000 0.005
0.000 0.005
0.000 0.005
*incomplete file
265
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BIOGRAPHICAL SKETCH
Stuart John Muller hails from South Africa, where he received an excellent
education at Hillcrest High School in KwaZulu-Natal. He matriculated as Head Boy and
proxime accessit dux, before subsequently acquiring a Bachelor of Science degree in
agricultural engineering from the University of Natal (the university and degree have
since been renamed to Bioresources Engineering and the University of KwaZulu-Natal,
respectively). There followed 18 months of global travel to Kenya, Tanzania, Zambia,
Botswana, United Kingdom (where he taught high-school students mathematics and
science), Nepal (where he trekked to Base Camp at Mount Everest), Thailand,
Cambodia, Australia, and New Zealand. In 2003, he moved to Florida to pursue a
Master of Science in Engineering degree in agricultural and biological engineering at the
University of Florida . Before he was able to complete his master’s, he was seduced by
an opportunity to embark on a Ph.D. in the same department . That was in 2004. He
would go on to claim the Guinness World Record for the World’s Longest Eyelash in
2007, and to eventually become a Doctor of Philosophy in 2010.
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